one would get a C "because grades need to be normally distributed." That the professor was describing a uniform distribution was a double irony) As a student, you are probably familiar Frarne L38l non andom samples, there are plenty of reasons to suspect that the distribution of grades would not be "normal." Misunderstandings about the normal distri- bution have occurred both in business and in the makers using this distribution. And, most impor tantly, always remember that the name normal distribution does not mean to suggest normal in the everyday (dare we say "normal"?) sense of the word! Problems for Section 6.2 LEARNING THE BASICS 6.1 Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), what is the probability that a. Z is less than 1.572 b. Z is greater than 1.847 c. Z is between 1.57 and 1.847 d. Z is less than 1.57 or greater than 1.84” 6.2 Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), what is the probability that a. Z is between -1.57 and 1.847 b. Z is less than -1.57 or greater than 1,847 c. What is the value of Z if only 2.5% of all possible Z val- ues are larger? d. Between what two values of Z (symmetrically distributed contained? around the mean) will 68.26% of all possible Z values be 6.3 Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), what is the probability that 8. Z is less than 1.08? b. Z is greater than -0,217 c. Z is less than -0.21 or greater than the mean? d. Z is less than -0.21 or greater than 1.08? 6.4 Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), deter- mine the following probabilities: 1. P(Z > 1.08) b. P(Z < -0.21) t P-196 < Z < -021) d. What is the value of Z if only 15.87% of all possible Z values are larger? 6.5 Given a normal distribution with 10, what is the probability that X>75? 100 and b. X < 70? c. X 80 or X 110? d. Between what two X values (symmetrically distributed around the mean) are 80% of the values? 6.6 Given a normal distribution with what is the probability that a. X> 437 h. X 427 c. 5% of the values are! d. Between what two $0) and σ = 4. than what Y value? values (symmetrically distributed around the mean) are 60% of the values? APPLYING THE CONCEPTS 6.7 In a recent year, about two-thirds of U.S. households purchased ground coffee. Consider the annual ground cof- fee expenditures for households purchasing ground coffee, assuming that these expenditures are approximately distrib- uted as a normal random variable with a mean of $65.16 and a standard deviation of $10.00. a. Find the probability that a household spent less than $35.00. $60.00. b. Find the probability that a household spent more than and $50.00? c. What proportion of the households spent between $40.00 d. 99% of the households spent less than what amount? SELF 6.8 Toby's Trucking Company determined that Test the distance traveled per truck per year is nor- mally distributed, with a mean of 50.0 thousand miles and a standard deviation of 12.0 thousand miles. a. What proportion of trucks can be expected to travel between 34.0 and 50.0 thousand miles in a year? b. What percentage of trucks can be expected to travel either below 30.0 or above 60.0 thousand miles in a year? trucks? c. How many miles will be traveled by at least 80% of the d. What are your answers to (a) through (c) if the standard deviation is 10.0 thousand miles? ILES FilelllCIELLED 1.20IVID Q Search L F3 F2 F1 Esc FO Main Office: 5702 30 Avenue Brooklyn, NY 11220 F4 F5 F6 F7 $ %