Exam 6: Normal Probability Distributions

If z is a standard normal variable, find the probability. -The probability that z lies between 0 and 3.01

Solve the problem. -If a continuous uniform distribution has parameters of $\mu = 0 \text { and } \sigma = 1$ then the minimum is $- \sqrt { 3 }$ and the maximum is $\sqrt { 3 }$ . For this distribution, find $\mathrm { P } ( - 1 < \mathrm { x } < 0.5 )$ Round your answer to three decimal places.

Solve the problem. -The probability of fewer than 43 democrats

Solve the problem. Round to the nearest tenth unless indicated otherwise. -Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7. Find P81, which separates the bottom 81% from the top 19%.

Solve the problem. -Three randomly selected households are surveyed as a pilot project for a larger survey to be conducted later. The numbers of people in the households are 1, 4, and 7. Consider the values of 1, 4, and 7 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 1, 4, and 7. The nine different samples are as follows: (1, 1), (1, 4), (1, 7), (4, 1), (4, 4), (4, 7), (7, 1), (7, 4), and (7, 7). (i) Construct a probability distribution table that describes the sampling distribution of the proportion of even numbers when samples of size n = 2 are randomly selected. (ii) Does the mean of the sample proportions target the value of the population proportion? (iii) Does the sample proportion make a good estimator of the population proportion?

The normal distribution has a greater percentage of its area close to the mean and much less in the tails. -Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test). Find P30, which is the IQ score separating the bottom 30% from the top 70%.

Solve the problem. -Three randomly selected households are surveyed as a pilot project for a larger survey to be conducted later. The numbers of people in the households are 2, 3, and 8. Consider the values of 2, 3, and 8 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 3, and 8. The nine different samples are as follows: (2, 2), (2, 3), (2, 8), (3, 2), (3, 3), (3, 8), (8, 2), (8, 3), and (8, 8). (i) Find the range of each of the nine samples, then summarize the sampling distribution of the ranges in the format of a table representing the probability distribution. (ii) Compare the population range to the mean of the sample ranges. (iii) Do the sample ranges target the value of the population range? In general, do ranges make good estimators of population ranges? Why or why not.?

Solve the problem. -Three randomly selected households are surveyed as a pilot project for a larger survey to be conducted later. The numbers of people in the households are 2, 4, and 10. Consider the values of 2, 4, and 10 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 4, and 10. The nine different samples are as follows: (2, 2), (2, 4), (2, 10), (4, 2), (4, 4), (4, 10), (10, 2), (10, 4), and (10, 10). (i) Find the mean of each of the nine samples, then summarize the sampling distribution of the means in the format of a table representing the probability distribution. (ii) Compare the population mean to the mean of the sample means. (iii) Do the sample means target the value of the population mean? In general, do means make good estimators of population means? Why or why not?

Solve the problem. -A normal quartile plot is given below for the lifetimes (in hours) of a sample of batteries of a particular brand. Use the plot to assess the normality of the lifetimes of these batteries. Explain your reasoning.

Solve the problem. -Human body temperatures are normally distributed with a mean of 98.20°F and a standard deviation of 0.62°F. If 19 people are randomly selected, find the probability that their mean body temperature will be less than 98)50°F.

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, exactly 225 are defective.

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. -In one county, the conviction rate for speeding is 85%. Estimate the probability that of the next 100 speeding summonses issued, there will be at least 90 convictions.

Solve the problem. -The ages (in years) of the four U.S. vice presidents who assumed office after presidential assassinations are 56 (A. Johnson), 51 (C. Arthur), 42 (T. Roosevelt), and 55 (L.B. Johnson). (i) Assuming that 2 of the ages are randomly selected with replacement, list the 16 different possible samples. (ii) Find the standard deviation of each of the 16 samples, then summarize the sampling distribution of the standard deviation in the format of a table representing the probability distribution. (iii) Compare the population standard deviation to the mean of the sample standard deviations. (iv) Do the sample standard deviations target the value of the population standard deviation? In general, do sample standard deviations make good estimators of population standard deviations? Why or why not?

Solve the problem. -Three randomly selected households are surveyed as a pilot project for a larger survey to be conducted later. The numbers of people in the households are 5, 6, and 9. Consider the values of 5, 6, and 9 to be a population. Assume that samples of size n = 2 are randomly selected with replacement from the population of 5, 6, and 9. The nine different samples are as follows: (5, 5), (5, 6), (5, 9), (6, 5), (6, 6), (6, 9), (9, 5), (9, 6), and (9, 9). (i) Find the median of each of the nine samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution. (ii) Compare the population median to the mean of the sample medians. (iii) Do the sample medians target the value of the population median? In general, do medians make good estimators of population medians? Why or why not?

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. -Shaded area is 0.4013.

Solve the problem. -The probability of at least 44 boys

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the probability of a rating that is between 200 And 275.

The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy last at least 300 days?

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.

A study of the amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado 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.