# Probability of normal distribution

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3. Delta airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes.

A. Show the graph of the probability density function for flight time

B. What is the probability that the flight will be no more than 5 minutes late?

C. What is the probability that the flight will be more than 10 minutes late?

D. What is the expected flight time?

5. The driving distance for the top 100 golfers on the PGA tour is between 284.7 and 310.6 yards. Assume that the driving distance for these golfers is uniformly distributed over this interval.

A. Give a mathematical expression for the probability density function of driving distance.

B. What is the probability the driving distance for one of these golfers is less than 290 yards?

C. What is the probability the driving distance for one of these golfers is at least 300 yards?

D. What is the probability the driving distance for one of these golfers is between 290 and

305 yards?

E. How many of these golfers drive the ball at least 290 yards?

9. A random variable is normally distributed with a mean of µ = 50 and a standard deviation of

= 5.

A. Sketch a normal curve for the probability density function. Label the horizontal axis with values of 35, 40, 45, 50, 55, 60, and 65. Figure 6.4 shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviation above the mean (in this case at 35 and 65.)

B. What is the probability the random variable will assume a value between 45 and 55?

C. What is the probability the random variable will assume a value between 40 and 60?

I know you don't see figure 6.4 because its in my textbook. sorry

17. The average amount parents and children spent per child on back-to-school clothes in Autumn 2001 was $527. Assume the standard deviation is $160 and that the amount spent is normally distributed.

A. What is the probability that the amount spent on a randomly selected child is more than $700?

B. What is the probability that the amount spent on a randomly selected child is less than $100?

C. What is the probability that the amount spent on a randomly selected child is between $450 and $700?

D. What is the probability that the amount spent on a randomly selected child is no more than $300?

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