5)According to a published study, 1 in every 4 men has been involved in a minor traffic accident. Suppose we have randomly and independently sampled twenty -five men and asked each whether he has been involved in a minor traffic accident. How many of the 25 men do we expect to have never been involved in a minor traffic accident? Round to the nearest whole number

6)A small life insurance company has determined that on the average it receives 3 death claims per day. Find the probability that the company receives at least seven death claims on a randomly selected day. Round your response to four decimal places

7)A machine is set to pump cleanser into a process at the rate of 9 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 8.5 to 9.5 gallons per minute. Find the probability that the machine pumps less than 8.75 gallons during a randomly selected minute. Round your response to two decimal places

8)A machine is set to pump cleanser into a process at the rate of 5 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 4.5 to 7.5 gallons per minute. Find the variance of the distribution. Round your response to two decimal places

9)The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2600 miles. If the manufacturer guarantees the tread life of the tires for the first 56,880 miles, what proportion of the tires will need to be replaced under warranty? Round your response to four decimal places

10)The weight of corn chips dispensed into a 10-ounce bag by the dispensing machine has been identified as possessing a normal distribution with a mean of 10.5 ounces and a standard deviation of .2 ounce. Suppose 100 bags of chips are randomly selected. Find the probability that the mean weight of these 100 bags exceeds 10.45 ounces. Round your response to 4 decimal places

11)Suppose a random sample of n = 64 measurements is selected from a population with mean = 65 and standard deviation = 12. Find the probability that falls between 65.75 and 68.75. round your response to four decimal places

12)A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will choose a random sample from the 100,000 items in the store's inventory in order to determine the proportion of merchandise that is outdated. The current owners have never determined the percentage of outdated merchandise and cannot help the buyers. How large a sample do the buyers need in order to be 90% confident that the margin of error of their estimate is within 5%