1. The distribution of scores on a recent test closely followed a Normal Distribution with a mean of 22 points and a standard deviation of 2 points. For this question, DO NOT apply the standard deviation rule.

(a) What proportion of the students scored at least 24 points on this test, rounded to five decimal places?

(b) What is the 29 percentile of the distribution of test scores, rounded to three decimal places?

2. A study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. It was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 2.60 days with an approximately normal distribution.

(a) Find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places.

(b) Find the probability that their hospital stay is greater than 6 days, rounded to five decimal places.

3. Suppose that 90% of all dialysis patients will survive for at least 5 years.

In a simple random sample of 100 new dialysis patients, what is the probability that the proportion surviving for at least five years will exceed 80%, rounded to 5 decimal places?

4. A factory produces plate glass with a mean thickness of 4mm and a standard deviation of 1.1mm. A simple random sample of 100 sheets of glass is to be measured, and the mean thickness of the 100 sheets is to be computed.

What is the probability that the average thickness of the 100 sheets is less than 4.06 mm? .

Round your answers to 5 decimal places.

5. 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 10 students from this distribution.

What is the probability that a SRS of 10 students will spend an average of between 600 and 700 dollars? Round to five decimal places.