1. Suppose a continuous random variableXis uniformly distributed between25 and 60. (a) Draw the graph of the uniform density function. (b) What is the probability that a randomly selected value will be above 45? (c) What is the probability that a randomly selected value will be less than 30? (d) What is the probability that a randomly selected value will be between 35 and50?

2. Polar Bear Frozen Food manufactures frozen French fries for sale to gro-cery store chains. The final package weight is thought to be a uniformly distributedrandom variable. Assume X, the weight of French fries, has a uniform distributionbetween 55 ounces and 70 ounces. (a) Draw the graph of the uniform density function.(b) What is the probability that a store will receive a package weighing less than 59ounces? (c) What is the probability that a package will contain between 60 and 65 ounces? (d) What is the probability that a package will contain exactly 60 ounces? (e) What is the mean weight for a package?

3. Find the z-scores that separate the middle 80% of the data from the area inthe tails of the standard normal distribution.

4. Find the value of z0.0755.

5. Determine the area under the standard normal curve that lies (a) to the left of z=0.92 (b) to the right of z=1.83 (c) between z= -1.08 and z= 2.05

6. Find the value of z such that 0.05 of the area under the curve lies to the right of z.

7. Assume that the random variable X is normally distributed with =50,ands=7. Find the probability that (a)P(X55) (b)P(X>40) (c)P(56X<68) (d)P(X=75)

8. Suppose that a national testing service gives a test in which the results arenormally distributed with a mean of 550 and standard deviation of 85. If you score a 625 on the test, what fraction of the students taking the test exceeded your score?

9. Professor G.G. believes that the grades for his statistics class have a normal distribution with a mean of 82 and a standard deviation of 8. (a) Find the score which separates the top 10% of the scores from the lowest 90% of the scores. (b) Professor G.G. plans to give all students who score in the top 10% of scores an A. Will a student who scored a 90 receive an A? Explain. (c) The professor plans to give all students who score in the lowest 10% of scores an F. Will a student who scored a 65 receive an F? Explain. (d) If the professor decides to pass all students who score in the top 70% of scores, what will be the minimum score a student should have to pass the course?

10. Suppose that the talk time on the latest Apple iPhone is approximately normally distributed with mean 7 hours and standard deviation 0.8 hrs. (a) What proportion of the time will a fully charged iPhone last at least 6 hours? (b) What is the probability a fully charged iPhone will last less than 5 hours? (c) What talk time would represent the cutoff for the top 5% of all talk times?(d) Would it be unusual for the phone to last more than 9 hours? Why?

11. Suppose the scores earned on Professor G.G's third Calculus grades are normally distributed with mean 64 and standard deviation 8. Professor G.G wants too curve the grade scores as follows: The top 6% get an A, the next 14% get a B, the middle 60% get a C, the bottom 6% fail, and the rest earn a D.

12. According to American Airlines, Flight 215 From Orlando to Los Angeles is on time 90% of the time. Randomly select 200 Flights and use the normal approxi-mation to the binomial to approximate (a) the probability that exactly 165 flights are on time. (b) the probability that at least 170 flights are on time. (c) the probability that fewer than 150 flights are on time. (d) the probability that between 135 and 180 flights, inclusive, are on time. (e) the probability that more than 180 flights are on time.