Stats

MAT 120 Quiz 3

Name: Summer 2020

Directions: Please show all work when possible, to increase your chance of partial credit. I will not give credit for answers with no justified work. Remember that the purpose of this quiz is to test your knowledge of the material, not your neighbors’. All answers must be simplified.

1. A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red (she can’t afford to get a ticket or cause an accident!). The number of lights that are red has the following probability distribution.

x P (x) 0 0.05 1 0.15 2 0.10 3 0.25 4 0.30 5 0.15

(a) Tomorrow morning, what is the probability that she will have to stop at less than 3 traffic lights on her way to work?

(b) Find the mean number of stops she has to make on her morning commute.

(c) Find the standard deviation of the number of stops.

2. Privacy is a concern for many users of the Internet. One survey showed that 59% of Internet users are somewhat concerned about the confidentiality of their e-mail. Based on this information, what is the probability that for a random sample of 10 Internet users, 6 are concerned about the privacy of their e-mail?

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3. Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that the test result is between -1.93 and 2.04.

4. Assume that men’s heights are normally distributed with a mean of 69.5 in and a standard deviation of 2.4 in.

(a) If a jet has a doorway height of 52.9 in, what percentage of men can fit through the door without bending?

(b) What doorway height would allow 78% of men to fit without bending?

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5. Based on a recent Harris Interactive survey, 23% of adults in the United States smoke. If a survey of 200 statistics students is conducted, find the probability that at least 58 of them smoke.

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