Question 1

The SAT is an exam used by colleges and universities to evaluate undergraduate applicants. The test scores are
normally distributed. In a recent year, the mean test score was 1475 and the standard deviation was 308. The
test scores of four students selected at random are 1930, 1340, 2150, and 1450.
a)Find the z-scores that correspond to each value
b)Determine whether any of the values are unusual.

Accepted Answer

The answer of The SAT is an exam used by...

Question 2

Determine whether the graph could represent a variable with a normal distribution. Explain your reasoning.

Accepted Answer

A) No, the graph is skewed right. 
B) No, the graph crosses the x-axis. 
C) No, the graph is skewed left. 
D) Yes, the graph fulfills the properties of the normal distribution

Question 3

Assume that the random variable X is normally distributed, with mean $\mu$ = 80 and standard deviation $\sigma$ = 15. Compute the probability $\mathrm { P } ( X > 92 )$

Accepted Answer

A) 0.2119 
B) 0.1977 
C) 0.7881 
D) 0.2420

Question 4

Find the area of the indicated region under the standard normal curve.

Accepted Answer

A) 0.1504 
B) 0.1292 
C) 0.8489 
D) 0.0212

Question 5

Use a standard normal table to find the z-score that corresponds to the cumulative area of 0.7019.

Accepted Answer

A) 0.53 
B) -0.53 
C) 0.835 
D) -0.835

Question 6

Assume that the salaries of elementary school teachers in the United States are normally distributed with a
mean of $29,000 and a standard deviation of $2000. What is the cutoff salary for teachers in the top 10%?

Accepted Answer

The answer of Assume that the salaries of elementary school...

Question 7

Assume that the heights of men are normally distributed with a mean of 69.5 inches and a standard deviation of 2.1 inches. If 36 men are randomly selected, find the probability that they have a mean height greater than
70.5 inches.

Accepted Answer

A) 0.0021 
B) 0.8188 
C) 0.9005 
D) 9.9671

Question 8

Find the probability of z occurring in the indicated region.
-

Accepted Answer

A) 0.2776 
B) 0.7224 
C) 0.2224 
D) 0.1894

Question 9

Find the probability of z occurring in the indicated region.
-

Accepted Answer

A) 0.0401 
B) 0.0668 
C) 0.9599 
D) 0.0228

Question 10

Use the standard normal distribution to find P(-2.25 < z < 1.25).

Accepted Answer

A) 0.8822 
B) 0.0122 
C) 0.4878 
D) 0.8944

Question 11

Find the area under the standard normal curve to the left of z = 1.5.

Accepted Answer

A) 0.9332 
B) 0.0668 
C) 0.5199 
D) 0.7612

Question 12

Ten percent of the population is left-handed. A class of 1800 students is selected. Convert the binomial probability $\mathrm { P } ( \mathrm { x } \geq 15 )$ to a normal probability by using the correction for continuity.

Accepted Answer

A)  $\mathrm { P } ( \mathrm { x } \geq 14.5 )$ 
B)  $\mathrm { P } ( \mathrm { x } < 14.5 )$ 
C)  $\mathrm { P } ( \mathrm { x } \leq 15.5 )$ 
D)  $\mathrm { P } ( \mathrm { x } \geq 15.5 )$

Question 13

Find the probability that in 200 tosses of a fair six-sided die, a five will be obtained at least 40 times.

Accepted Answer

A) 0.1210 
B) 0.8810 
C) 0.0871 
D) 0.3875

Question 14

In a certain normal distribution, find the standard deviation ? when $\mu$ = 50 and 10.56% of the area lies to the right of 55.

Accepted Answer

A) 4 
B) 2 
C) 3 
D) 5

Question 15

Find the z-scores for which 98% of the distributionʹs area lies between -z and z.

Accepted Answer

A) (-2.33, 2.33) 
B) (-1.645, 1.645) 
C) (-1.96, 1.96) 
D) (-0.99, 0.99)

Question 16

The mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes is $5600. The distribution of incomes is skewed to the right. Find the mean and standard error of the mean for
This sampling distribution when using random samples of size 66. Round your answers to the nearest dollar.

Accepted Answer

A) $28,520, $689 
B) $28,520, $5600 
C) $28,520, $66 
D) $28,520, $85

Question 17

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the x-score that corresponds to a z-score of -1.645.

Accepted Answer

A) 75.3 
B) 79.1 
C) 82.3 
D) 91.0

Question 18

The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.60° F. If 36 adults are randomly selected, find the probability that their mean body temperature is greater
Than 98.4° F.

Accepted Answer

A) 0.9772 
B) 0.0228 
C) 0.8188 
D) 0.9360

Question 19

A recent survey found that 72% of all adults over 50 wear glasses for driving. You randomly select 33 adults
over 50, and ask if he or she wears glasses. Decide whether you can use the normal distribution to approximate
the binomial distribution. If so, find the mean and standard deviation, If not, explain why.

Accepted Answer

The answer of A recent survey found that 72% of...

Question 20

Find the area under the standard normal curve between z = 1 and z = 2.

Accepted Answer

A) 0.1359 
B) 0.8413 
C) 0.5398 
D) 0.2139

Exam 5: Normal Probability Distributions

Determine whether the graph could represent a variable with a normal distribution. Explain your reasoning.

Assume that the random variable X is normally distributed, with mean $\mu$ = 80 and standard deviation $\sigma$ = 15. Compute the probability $\mathrm { P } ( X > 92 )$

Find the area of the indicated region under the standard normal curve.

Use a standard normal table to find the z-score that corresponds to the cumulative area of 0.7019.

Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $29,000 and a standard deviation of $2000. What is the cutoff salary for teachers in the top 10%?

Assume that the heights of men are normally distributed with a mean of 69.5 inches and a standard deviation of 2.1 inches. If 36 men are randomly selected, find the probability that they have a mean height greater than 70.5 inches.

Find the probability of z occurring in the indicated region. -

Find the probability of z occurring in the indicated region. -

Use the standard normal distribution to find P(-2.25 < z < 1.25) .

Find the area under the standard normal curve to the left of z = 1.5.

Ten percent of the population is left-handed. A class of 1800 students is selected. Convert the binomial probability $\mathrm { P } ( \mathrm { x } \geq 15 )$ to a normal probability by using the correction for continuity.

Find the probability that in 200 tosses of a fair six-sided die, a five will be obtained at least 40 times.

In a certain normal distribution, find the standard deviation ? when $\mu$ = 50 and 10.56% of the area lies to the right of 55.

Find the z-scores for which 98% of the distributionʹs area lies between -z and z.

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the x-score that corresponds to a z-score of -1.645.

The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.60° F. If 36 adults are randomly selected, find the probability that their mean body temperature is greater Than 98.4° F.

Find the area under the standard normal curve between z = 1 and z = 2.

Exam 5: Normal Probability Distributions

Determine whether the graph could represent a variable with a normal distribution. Explain your reasoning.

Assume that the random variable X is normally distributed, with mean μ\muμ = 80 and standard deviation σ\sigmaσ = 15. Compute the probability P(X>92) \mathrm { P } ( X > 92 ) P(X>92)

Find the area of the indicated region under the standard normal curve.

Use a standard normal table to find the z-score that corresponds to the cumulative area of 0.7019.

Assume that the salaries of elementary school teachers in the United States are normally distributed with a mean of $29,000 and a standard deviation of $2000. What is the cutoff salary for teachers in the top 10%?

Assume that the heights of men are normally distributed with a mean of 69.5 inches and a standard deviation of 2.1 inches. If 36 men are randomly selected, find the probability that they have a mean height greater than 70.5 inches.

Find the probability of z occurring in the indicated region. -

Find the probability of z occurring in the indicated region. -

Use the standard normal distribution to find P(-2.25 < z < 1.25) .

Find the area under the standard normal curve to the left of z = 1.5.

Ten percent of the population is left-handed. A class of 1800 students is selected. Convert the binomial probability P(x≥15) \mathrm { P } ( \mathrm { x } \geq 15 ) P(x≥15) to a normal probability by using the correction for continuity.

Find the probability that in 200 tosses of a fair six-sided die, a five will be obtained at least 40 times.

In a certain normal distribution, find the standard deviation ? when μ\muμ = 50 and 10.56% of the area lies to the right of 55.

Find the z-scores for which 98% of the distributionʹs area lies between -z and z.

IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the x-score that corresponds to a z-score of -1.645.

The body temperatures of adults are normally distributed with a mean of 98.6° F and a standard deviation of 0.60° F. If 36 adults are randomly selected, find the probability that their mean body temperature is greater Than 98.4° F.

Find the area under the standard normal curve between z = 1 and z = 2.

Assume that the random variable X is normally distributed, with mean $\mu$ = 80 and standard deviation $\sigma$ = 15. Compute the probability $\mathrm { P } ( X > 92 )$

Ten percent of the population is left-handed. A class of 1800 students is selected. Convert the binomial probability $\mathrm { P } ( \mathrm { x } \geq 15 )$ to a normal probability by using the correction for continuity.

In a certain normal distribution, find the standard deviation ? when $\mu$ = 50 and 10.56% of the area lies to the right of 55.