Question 1

If Z is a standard normal variable, find the probability
-P(Z > 0.59)

Accepted Answer

A) 0.2190 
B) 0.2224 
C) 0.2776 
D) 0.7224 
A) 0.2190 
B) 0.2224 
C) 0.2776 
D) 0.7224

Question 2

A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is the probability of being correct 14 or more times by guessing? Does this probability seem to verify her claim?

Accepted Answer

A) .4418 , yes 
B) .0582 , no 
C) .0582 , yes 
D) .4418 , no 
A) .4418 , yes 
B) .0582 , no 
C) .0582 , yes 
D) .4418 , no

Question 3

For the binomial distribution with the given values for n and p
-n = 53 and p = .7

Accepted Answer

A) Normal approximation is suitable. 
B) Normal approximation is not suitable. 
A) Normal approximation is suitable. 
B) Normal approximation is not suitable.

Question 4

Assume that X has a normal distribution, and find the indicated probability.
-The mean is $\mu = 15.2$ and the standard deviation is $\sigma = 0.9$. Find the probability that $X$ is greater than 17.

Accepted Answer

A) 0.9713 
B) 0.9772 
C) 0.0228 
D) 0.9821 
A) 0.9713 
B) 0.9772 
C) 0.0228 
D) 0.9821

Question 5

If Z is a standard normal variable, find the probability
-The probability that Z lies between -2.41 and 0

Accepted Answer

A) 0.4920 
B) 0.4910 
C) 0.5080 
D) 0.0948 
A) 0.4920 
B) 0.4910 
C) 0.5080 
D) 0.0948

Question 6

Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost
-Between 7 pounds and 10 pounds

Accepted Answer

A)  $\frac { 2 } { 3 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  $\frac { 2 } { 3 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $\frac { 1 } { 4 }$ 
D)  $\frac { 1 } { 2 }$

Question 7

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-Estimate the probability of getting exactly 43 boys in 90 births.

Accepted Answer

A) 0.0729 
B) 0.0764 
C) 0.0159 
D) 0.1628 
A) 0.0729 
B) 0.0764 
C) 0.0159 
D) 0.1628

Question 8

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°C at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information.
-If 7% of the thermometers are rejected because they have readings that are too low, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others.

Accepted Answer

A) -1.39° 
B) -1.26° 
C) -1.48° 
D) -1.53° 
A) -1.39° 
B) -1.26° 
C) -1.48° 
D) -1.53°

Question 9

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, at least 219 are defective.

Accepted Answer

A) 0.0823 
B) 0.9066 
C) 0.0934 
D) 0.0869 
A) 0.0823 
B) 0.9066 
C) 0.0934 
D) 0.0869

Question 10

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate.

Accepted Answer

A) 0.0679 
B) 0.0669 
C) 0.9331 
D) 0.0769 
A) 0.0679 
B) 0.0669 
C) 0.9331 
D) 0.0769

Question 11

Solve the problem.
-A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 7.6 hours.

Accepted Answer

A) 0.0008 
B) 0.0036 
C) 0.0025 
D) 0.0103 
A) 0.0008 
B) 0.0036 
C) 0.0025 
D) 0.0103

Question 12

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution.
-With n = 20 and p = 0.60, estimate P(fewer than 8).

Accepted Answer

A) 0.0668 
B) 0.4332 
C) 0.0202 
D) 0.4953 
A) 0.0668 
B) 0.4332 
C) 0.0202 
D) 0.4953

Question 13

If Z is a standard normal variable, find the probability
-The probability that Z is greater than -1.82

Accepted Answer

A) 0.9656 
B) -0.0344 
C) 0.4656 
D) 0.0344 
A) 0.9656 
B) -0.0344 
C) 0.4656 
D) 0.0344

Question 14

Construct a normal probability plot of the given data. Use your plot to determine whether the data come from a normally distributed population
-The heart rates (in beats per minute)of 30 randomly selected students are given below. $$\begin{array} { l l l l l } 
78 & 64 & 69 & 75 & 80 \
63 & 70 & 72 & 72 & 68 \
77 & 71 & 74 & 84 & 70 \
62 & 67 & 71 & 69 & 58 \
74 & 70 & 80 & 63 & 88 \
60 & 68 & 69 & 70 & 71
\end{array}$$

Accepted Answer

The requirement for normality

Question 15

Provide an appropriate response.
-Under what conditions can we apply the results of the central limit theorem?

Accepted Answer

Either the sample size must be

Question 16

Construct a normal probability plot of the given data. Use your plot to determine whether the data come from a normally distributed population
-The amount of rainfall (in inches)in 25 consecutive years in a certain city. $\begin{array} { l l l l l } 20.4 & 25.1 & 22.8 & 27.0 & 23.5 \end{array}$
$\begin{array} { l l l l l } 24.2 & 26.0 & 25.6 & 23.3 & 24.1 \end{array}$
$\begin{array} { l l l l l } 21.9 & 27.6 & 24.7 & 25.3 & 21.6 \end{array}$
$\begin{array} { l l l l l } 31.0 & 23.6 & 26.1 & 25.5 & 24.8 \end{array}$
$\begin{array} { l l l l l } 18.1 & 22.4 & 24.9 & 30.0 & 29.3 \end{array}$

Accepted Answer

The requirement for normality

Question 17

Provide an appropriate response.
-Explain how a nonstandard normal distribution differs from the standard normal distribution. Describe the process for finding probabilities for nonstandard normal distributions.

Accepted Answer

Both distributions are bell-shaped. In a

Question 18

The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $150. What percentage of trainees earn less than $900 a month?

Accepted Answer

A) 9.18% 
B) 40.82% 
C) 35.31% 
D) 90.82% 
A) 9.18% 
B) 40.82% 
C) 35.31% 
D) 90.82%

Question 19

Provide an appropriate response.
-State the Empirical Rule. Use the standard normal distribution to explain the percent values given in the Empirical Rule.

Accepted Answer

The answer of Provide an appropriate response.
-State the Empirical Rule....

Question 20

Find the probability that in 200 tosses of a fair die, we will obtain at least 40 fives.

Accepted Answer

A) .0871 
B) .2229 
C) .1210 
D) .3871 
A) .0871 
B) .2229 
C) .1210 
D) .3871

If Z is a standard normal variable, find the probability -P(Z > 0.59)

A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is the probability of being correct 14 or more times by guessing? Does this probability seem to verify her claim?

For the binomial distribution with the given values for n and p -n = 53 and p = .7

Assume that X has a normal distribution, and find the indicated probability. -The mean is $\mu = 15.2$ and the standard deviation is $\sigma = 0.9$ . Find the probability that $X$ is greater than 17.

If Z is a standard normal variable, find the probability -The probability that Z lies between -2.41 and 0

Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost -Between 7 pounds and 10 pounds

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -Estimate the probability of getting exactly 43 boys in 90 births.

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, at least 219 are defective.

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate.

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -With n = 20 and p = 0.60, estimate P(fewer than 8).

If Z is a standard normal variable, find the probability -The probability that Z is greater than -1.82

Provide an appropriate response. -Under what conditions can we apply the results of the central limit theorem?

Provide an appropriate response. -Explain how a nonstandard normal distribution differs from the standard normal distribution. Describe the process for finding probabilities for nonstandard normal distributions.

The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $150. What percentage of trainees earn less than $900 a month?

Provide an appropriate response. -State the Empirical Rule. Use the standard normal distribution to explain the percent values given in the Empirical Rule.

Find the probability that in 200 tosses of a fair die, we will obtain at least 40 fives.

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Probability Distributions

Estimates and Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Multinomial Experiments and Contingency Tables

Analysis of Variance

Nonparametric Statistics

Statistical Process Control

Filters

Exam 6: Normal Probability Distributions

If Z is a standard normal variable, find the probability -P(Z > 0.59)

A coin is tossed 20 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 14 tosses. What is the probability of being correct 14 or more times by guessing? Does this probability seem to verify her claim?

For the binomial distribution with the given values for n and p -n = 53 and p = .7

Assume that X has a normal distribution, and find the indicated probability. -The mean is μ=15.2\mu = 15.2μ=15.2 and the standard deviation is σ=0.9\sigma = 0.9σ=0.9 . Find the probability that XXX is greater than 17.

If Z is a standard normal variable, find the probability -The probability that Z lies between -2.41 and 0

Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost -Between 7 pounds and 10 pounds

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -Estimate the probability of getting exactly 43 boys in 90 births.

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -Two percent of hair dryers produced in a certain plant are defective. Estimate the probability that of 10,000 randomly selected hair dryers, at least 219 are defective.

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -The probability that a radish seed will germinate is 0.7. Estimate the probability that of 140 randomly selected seeds, exactly 100 will germinate.

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -With n = 20 and p = 0.60, estimate P(fewer than 8).

If Z is a standard normal variable, find the probability -The probability that Z is greater than -1.82

Provide an appropriate response. -Under what conditions can we apply the results of the central limit theorem?

Provide an appropriate response. -Explain how a nonstandard normal distribution differs from the standard normal distribution. Describe the process for finding probabilities for nonstandard normal distributions.

The incomes of trainees at a local mill are normally distributed with a mean of $1100 and a standard deviation of $150. What percentage of trainees earn less than $900 a month?

Provide an appropriate response. -State the Empirical Rule. Use the standard normal distribution to explain the percent values given in the Empirical Rule.

Find the probability that in 200 tosses of a fair die, we will obtain at least 40 fives.

Introduction to Statistics

Summarizing and Graphing Data

Statistics for Describing, Exploring, and Comparing Data

Probability

Probability Distributions

Estimates and Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Multinomial Experiments and Contingency Tables

Analysis of Variance

Nonparametric Statistics

Statistical Process Control

Filters

Assume that X has a normal distribution, and find the indicated probability. -The mean is $\mu = 15.2$ and the standard deviation is $\sigma = 0.9$ . Find the probability that $X$ is greater than 17.