BER 345 Homework #5 Covers Sections 6.1, 6.2, and 6.3 1. Using the Standard Normal Distribution (Table E in Appendix C), find each probability: a. P(0 < z < 2.25) b. P(-1.75 < z < 0) c. P(-1.65 < z < 2.12) d. P(1.35 < z < 1.87) e. P(-2.56 < z < 0.32) f. P(z > 1.69) g. P(z < -2.12) h. P(z > -1.15) i. P(z < 1.84) j. P(z > -1.73) 2. The average salary for graduates entering the actuarial field is $40,000 ( ). If the salaries are normally distributed with a standard deviation of $5000 ( = 5000), find the probability that: a. An individual graduate (n = 1) will have a salary over $44,500: P(X > 44,500). b. A group of nine graduates (n = 9) will have an average over $44,500: P( 3. The average weight of an airline passenger's suitcase is 45 pounds ( ) . The standard deviation is 2 pounds ( = 2). If 20% of the suitcases are overweight, find the maximum weight allowed by the airline. That is, find the 80 th percentile, which is the X that represents the weight of the suitcase. Assume that the variable is normally distributed. 4. The average cost of XYZ brand running shoes is $85 per pair ( , with a standard deviation of $8 ( = 8). If nine pairs of running shoes are selected (n = 9), find the probability that the mean cost of a pair of shoes will be less than $80: P( . Assume that the variable is normally distributed. 5. In a recent year, Deleware had the highest per capita annual income with $51,803 ( If = $4850, find the mean . that falls at the 85th percentile for a sample of 35 residents? 6. The national average for the SAT is 1028 ( Find the Percentile for a score of 1065 for: a. A single student (n=1) b. For a mean of 50 student (n=50) and the standard deviation is 100 ( = 100). c. For a mean of 500 students (n=500) 7. Of all 3- to 5-year old children, 56% are enrolled in school. We are looking at a sample of 500 such children, and this is thought to follow a binomial distribution. Use the normal approximation to the binomial to find the probability that at least 290 of those children will be enrolled in school