Consider the probability that more than 99 out of 159 people have not been in a car accident. Assume the probability that a given person has not been in a car accident is 61%. Approximate the probability using the normal distribution.

Consider the probability that more than 92 out of 160 flights will be on-time. Assume the probability that a given flight will be on-time is 65%.

Approximate the probability using the normal distribution. Round your answer to four decimal places.

Assume a binomial probability distribution with n=40 and pie symbol =0.26. Compute the following, a) the mean and standard deviation of the random variable b) the probability that x is 13 or more. c)the probability that x is 7 or less.

3. A box contains 15 resistors. Ten of them are labeled 50 ohms and the other five are labeled 100 ohms. a. What is the probability that the first resistor is 100 ohms? b. What is the probability that the second resistor is 100 ohms, given that the first resistor is 50 ohms? c. What is the probability that the second resistor is 100ohms, given that the first resistor is 100 ohms?

4. Refer to Exercise 3. Resistors are randomly selected from the box, one by one, until a 100ohm resistor is selected. a. What is the probability that the first two resistors are both 50 ohms? b. What is the probability that a total of two resistors are selected from the box? c. What is the probability that more than three resistors are selected from the box?

Tyler lives in Anchorage and has loss averse preferences. In particular, Tyler values a gain of amount x as u(x) = x^1/2 and values a loss of −x as u(−x) = −2x^1/2

(a) What is the maximum amount of money that Tyler would pay for a lottery that pays $1000 with probability 1/2 and $0 with probability 1/2 ?

(b) What is the maximum amount of money that Tyler would pay to avoid playing a lottery that loses $1000 with probability 1/2 and loses $0 with probability 1/2 ?

(c) What is the maximum amount of money that Tyler would pay to avoid playing a lottery that loses $1000 with probability 1/2 and gains $1000 with probability 1/2 ?

Applegate Inc. has developed a new shampoo with a distinctive fragrance. Before distributing it nationally, Applegate will test market the new product. The joint probability of a successful test market and high sales upon national distribution is 0.5. The joint probability of a successful test market and low sales nationally is 0.1. The joint probabilities of an unsuccessful test market and either high or low sales are both 0.2.

Construct a joint probability table and then answer the following questions.

An automobile insurance company divides customers into three categories, good risks, medium risks, and poor risks. Assume that 74% of the customers are good risks, 20% are medium risks, and 6% are poor risks. Assume that during the course of a year, a good risk customer has probability 0.005 of filing an accident claim, a medium risk customer has probability 0.01, and a poor risk customer has probability 0.025. A customer is chosen at random.

What is the probability that the customer is a good risk and has filed a claim? Round the answer to four decimal places.

What is the probability that the customer has filed a claim? Round the answer to four decimal places.

Given that the customer has filed a claim, what is the probability that the customer is a good risk?