Exam 6: Normal Probability Distributions

Assume that X has a normal distribution, and find the indicated probability. -The mean is $\mu = 15.2$ .2 and the standard deviation is $\sigma = 0.9$ Find the probability that X is greater than 15.2.

Find the indicated probability. -The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?

SAT verbal scores are normally distributed with a mean of 430 and a standard deviation of 120 (based on data from the College Board ATP). (a) If a single student is randomly selected, find the probability that the sample mean is above 500. (b) If a sample of 35 students are selected randomly, find the probability that the sample mean is above 500. These two problems appear to be very similar. Which problem requires the application of the central limit theorem, and in what way does the solution process differ between the two problems?

You will use a normal distribution to approximate a binomial distribution. Complete the following table for a distribution in which $\mu = 16$ 16. It might be helpful to make a diagram to help you determine the continuity factor for each entry. Find the probability that The continuity correction factor is: x is at least 12 x is at most 12 x is more than 12 x is less than 12

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of $0 ^ { \circ } \mathrm { C }$ 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 $0 ^ { \circ } \mathrm { C }$ (denoted by negative numbers) and some give readings above $0 ^ { \circ } \mathrm { C }$ (denoted by positive numbers). Assume that the mean reading is $0 ^ { \circ } \mathrm { C }$ and the standard deviation of the readings is $1.00 ^ { \circ } \mathrm { C }$ 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 high, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others.

For the binomial distribution with the given values for n and p, state whether or not it is suitable to use the normal distribution as an approximation. -n = 20 and p = 0.9

Solve the problem. -For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. If 23 women aged 18-24 are randomly selected, find the probability that their Mean systolic blood pressure is between 119 and 122.

The continuity correction is used to compensate for the fact that a ________ distribution is used to approximate a ________ distribution.

Solve the problem. -The ages of 30 students selected randomly from one college are as follows: 21 23 20 24 20 19 20 19 22 32 20 24 26 21 37 23 18 34 25 30 22 24 23 19 28 20 29 21 35 25 20 21 28 22 32

Heights of adult females are normally distributed. Samples of height of adult females, each of size n = 3, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as a normal distribution because the sample size is so small? Explain.

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

Find the indicated probability. -Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal Quarters will be rejected?

The normal distribution has a greater percentage of its area close to the mean and much less in the tails. -Find the indicated IQ score. The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). The shaded area under the curve is 0.10.

Solve the problem. -A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 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 8.9 hours.

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses, estimate the probability of getting at least 20% correct.

Solve the problem. Round to the nearest tenth unless indicated otherwise. -The serum cholesterol levels for men in one age group are normally distributed with a mean of 178.1 and a standard deviation of 40.4. All units are in mg/100 mL. Find the two levels that separate the top 9% and the Bottom 9%.

Solve the problem. -A poll of 1200 randomly selected students in grades 6 through 8 was conducted and found that 59% enjoy playing sports. What is the sampling distribution suggested by the given data?

A normal quartile plot is given below for the weekly incomes (in dollars) of a sample of engineers in one town. Describe what each x value represents and what each y value represents. Use the plot to assess the normality of the incomes of engineers in this town. Explain your reasoning.

If z is a standard normal variable, find P(z > 0.97).

If a sample size is < ________, the sample size must come from a population having a normal distribution in order to follow normal distribution calculations.