Chapter 5 Statistics

Suppose X is a random variable described by a uniform probability distribution with c=30 and d=80. Find the probability P(20<X<100)? A. 1.0 B. 0.8 C. 0.6 D. 1.6

????????? A. 1.0

If the scores of an exam follow a normal distribution with mean 75 and standard deviation 5, what is the proportion of students you would expect to have scores more than 85 or less than 65? A. 0.05 B. 0.68 C. 0.95 D. 0.025

A. 0.05

Almost all companies utilize some type of year-end performance review for their employees. Human Resource (HR) at a university's Health Science Center provides guidelines for supervisors rating their subordinates. For example, raters are advised to examine their ratings for a tendency to be either too lenient or too harsh. According to HR, ``if you have this tendency, consider using a normal distribution -- 10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable.'' Suppose you are rating an employee's performance on a scale of 1 (lowest) to 100 (highest). Also, assume the ratings follow a normal distribution with a mean of 50 and a standard deviation of 20. What is the lowest rating you should give to an ``exemplary'' employee if you follow the university's HR guidelines? A. 76 B. 85 C. 90 D. 25

A. 76

If a population data set is normally distributed, what is the proportion of measurements you would expect to fall two standard deviation below the mean? A. 0.68 B. 0.975 C. 0.025 D. 0.32

C. 0.025

Suppose X is a random variable described by a uniform probability distribution with c=30 and d=80. What is the mean of X? A. 52.5 B. 55 C. 25 D. 100

Mean: μ= c+d/ 2 μ= 30 + 80/ 2 = 55 B. 55

Suppose X is a random variable described by a uniform probability distribution with c=30 and d=80. Find the probability P(40<X<80)? A. 0.2 B. 0.8 C. 0.6 D. 0.4

P(a<x<b)= b-a / d-c P= 80-40 / 80-30 = 0.8 B. 0.8

Suppose X is a random variable described by a uniform probability distribution with c=30 and d=80. Find the probability P(20<X<40)? A. 0.4 B. 0.2 C. 0.6 D. 0.8

X cannot be any value less than 30 or larger than 80 P(20 < X < 40) = P(30 < X < 40) = (40-30)/(80-30)=10/50=0.2 B. 0.2

Suppose X is a random variable described by a uniform probability distribution with c=30 and d=80. Find f(x). A. f(x) = 1/110, 30 <= x <= 80 B. f(x) = 1/50, 30 <= x <= 80 C. f(x) = 1/50, 35 <= x <= 70 D. f(x) = 1/110, 35 <= x <= 70

f(x) = 1/ d-c f(x)= 1/ 80-30= 0.02 = 1/50 B. f(x) = 1/50, 30 <= x <= 80

The mean and standard deviation of the ages of a groups of 50 women are 51 years and 5 years, respectively. One women is randomly selected from the group, and her age is observed. Find the probability that her age will fall between 41 and 61. Which of the following statements is most appropriate. A. Using a normal table, we can find the probability is 0.9545. B. Using the empirical rule, the probability is approximately 0.95. C. Using Chebyshev's rule, the probability is at least 0.75. D. 0.5

C. Using Chebyshev's rule, the probability is at least 0.75.

If a population data set is normally distributed, what is the proportion of measurements you would expect to fall within one standard deviation of the mean? A. 0.90 B. 0.95 C. 1.00 D. 0.68

D. 0.68