Suppose that the distribution for total amounts spent by students vacationing for a week in Florida is normally distributed with a mean of 650 and a standard deviation of 120. Suppose you take a simple random sample (SRS) of 25 students from this distribution. What is the probability that a SRS of 25 students will spend an average of between 600 and 700 dollars? Round to five decimal places.

The NJ Department of Health has reported the average life span of NJ residents is 81 years. If the standard deviation is σ = 4 years, what is the probability of a person living to at least 92 years of age?

A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. They collect a simple random sample of 50 bottles and obtain a sample mean of 16.07 ounces and a sample standard deviation of 0.10 ounces. At a 0.01 level of significance, test the claim that the mean amount of juice in a bottle is less than 16.1 ounces.

Suppose the mean income of firms in the industry for a year is 2525 million dollars with a standard deviation of 77 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn less than 4040 million dollars? Round your answer to four decimal places.

Suppose a batch of steel rods produced at a steel plant have a mean length of 178 millimeters, and a standard deviation of 12 millimeters. If 76 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by less than 0.56 millimeters? Round your answer to four decimal places.

Suppose the mean income of firms in the industry for a year is 80 million dollars with a standard deviation of 55 million dollars. If incomes for the industry are distributed normally, what is the probability that a randomly selected firm will earn more than 88 million dollars? Round your answer to four decimal places.

* Your answer is incorrect. Service time for a customer coming through a checkout counter in a retail store is a random variable with the mean of 3.5 minutes and standard deviation of 3.5 minutes. Suppose that the distribution of service time is fairly close to a normal distribution. Suppose there are two counters in a store, n₁ = 2 customers in the first line and n₂ = 13 customers in the second line. Find the probability that the difference between the mean service time for the shorter line X₁ and the mean service time for the longer one X₂ is more than 0.1 minutes. Assume that the service times for each customer can be regarded as independent random variables. Round your answer to two decimal places (e.g. 98.76). P = i 98.80