Question

1. Given that x is a normal variable with mean μ = 112 and standard deviation...

1. Given that x is a normal variable with mean μ = 112 and standard deviation σ = 14, find the following probabilities. (Round your answers to four decimal places.)

(a)  P(x ≤ 120)

(b)  P(x ≥ 80)

(c)  P(108 ≤ x ≤ 117)

2. Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.8 minutes and a standard deviation of 1.9 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)

(a) the response time is between 5 and 10 minutes


(b) the response time is less than 5 minutes


(c) the response time is more than 10 minutes

3. In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

Do you take the free samples offered in supermarkets? About 58% of all customers will take free samples. Furthermore, of those who take the free samples, about 41% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you were offering free samples, 301 customers passed by your counter. (Round your answers to four decimal places.)

(a) What is the probability that more than 180 will take your free sample?


(b) What is the probability that fewer than 200 will take your free sample?


(c) What is the probability that a customer will take a free sample and buy the product? Hint: Use the multiplication rule for dependent events. Notice that we are given the conditional probability P(buy|sample) = 0.41, while P(sample) = 0.58.


(d) What is the probability that between 60 and 80 customers will take the free sample and buy the product? Hint: Use the probability of success calculated in part (c).

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