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1. Professor Smith's statistics midterm had a mean of 85 and a standard deviation of 8. If a student got a score of 73, what was the student's standardized (z) score?
2. What is the probability of a normal random variable taking a value more than 1.6 standard deviations above its mean?
3. What is the probability that a normal random variable will take a value between 2 standard deviations below its mean and 1 standard deviation above its mean? [In other words, between Z = -2 and Z = 1]
4. The probability is .5 that a standardized normal variable takes a value below what particular value of Z?
5. The probability is .1515 that a standardized normal variable takes a value above what particular value of Z?
6. What two Z values, symmetric around the mean, will contain 75.4% of all Z values?
7. X is a normally distributed random variable with a mean of 50 and a standard deviation of 2. What is the probability that X is less than 45?
8. A company that sells annuities must base the annual payout on the probability distribution of the length of life of the participants in the plan. Suppose the probability distribution of the lifetimes of the participants is a normal distribution with a mean of 70 years and a standard deviation of 3.5 years. What proportion of the plan recipients would receive payments beyond age 75?
9. The owner of a fish market learns that the mean weight for salmon is 12.3 pounds, with a standard deviation of 3 pounds. Assuming that the weights of salmon are normally distributed, what is the probability that a randomly selected salmon will weigh less than 10 pounds?
10. (Use the salmon information from previous problem.) The middle 95% of salmon will weigh between ____ pounds and ____ pounds.
[Don't forget the question is asking for pounds.]
Approximately 10% of people are left-handed. If two people are selected at random, what is the probability of the following events?a. Both are right-handed.b. Both are left-handed.c. One is right-handed and the other is left-handed.
How many 6 digit numbers are there with exact three different digits each repeated twice. example: 255277, 112233,123123
Determine the posterior probabilities, given the following prior and likelihood probabilities.Prior probabilities P(s1) = .25 P(s2) = .40 P(s3) = .35 Likelihood Probabilities
Question: 1) Suppose that the frequency distribution of daily high temperatures in a city are normally distributed with a mean of 60 degrees. Suppose that roughly one day every two years has a high temperature of 90-degrees or warmer. If this is the ..
Way around B&W plots
Given a normal distribution with µ =50 and σ =4, what is the probability that a. X > 43?b. X
If the results on a nationally administered introductory statistics exam is normally distributed with a mean of 100 points and a standard deviation of eight points determine the following: a. describe the graph of the distribution b. find at the Z sc..
If the budget analyst wanted to build a regression model using only two independent variables to predict nursing salaries, what variables should be used?
Mickey Lawson is considering investing some money that he inherited. The following payoff table gives the profits that would be realized during the next year for each of three investment alternatives Mickey is considering:
A fast-food chain randomly attaches coupons for prizes to the packages used to serve french fries. Most of the coupons say "Play again," but a few are winners. Of the coupons, 52 percent pay nothing, with the rest evenly divided between "Win a free o..
What are the assumptions made in performing the hypothesis test in Question 3? Are these assumptions reasonable? Provide explanation to substantiate your view.
Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of $6,500. We randomly survey ten teachers from that district. a. Find the 90th percentile for an individual te..
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