bus statistics

Use Excel to perform the calculations needed for this assignment

Section 6.1

1. The random variable x is known to be uniformly distributed between 1.0 and 1.5.

a) Show the graph of the probability density function.

b) Compute P(x = 1.25)

c) Compute P(1.0 ≤ x ≤ 1.25)

d) Compute P(1.20 < x < 1.5)

2. The random variable x is known to be uniformly distributed between 10 and 20.

a) Show the graph of the probability density function.

b) Compute P(x < 15)

c) Compute P(12 ≤ x ≤ 18)

3. 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?

4. On average, 30-minute television sitcoms have 22 minutes of programing (the remainder is commercials). Assume that the probability distribution for minutes of programing can be approximated by a uniform distribution from 18 minutes to 26 minutes.

a) What is the probability that a sitcom will have 25 or more minutes of programming?

b) What is the probability that a sitcom will have between 21 and 25 minutes of programming?

c) What is the probability that a sitcom will have more than 10 minutes or commercials?

Section 6.2

5. Draw a graph of the standard normal distribution. Label the horizontal axis at values of

-3, -2, -1, 0, 1, 2, 3. Then compute each of the following probabilities:

a) P( z ≤ 1.5)

b) P( z ≤ 1)

c) P(1 ≤ z ≤ 1.5)

d) P( 0 < z < 2.5)

6. Given that z is a standard random variable, compute the following probabilities.

a) P( z ≤ -1.0)

b) P( z ≥ -1)

c) P( z ≥ -1.5)

d) P( -2.5 ≤ z)

e) P(-3 < z ≤ 0)

7. Given that z is a standard random variable, compute the following probabilities.

a) P(0 < z ≤ 0.83)

b) P(-1.57 ≤ z ≤ 0)

c) P( z > 0.44)

d) P( z ≤ -0.71)

8. Given that z is a standard random variable, find z for each situation.

a) The area to the left of z is 0.9750

b) The area between 0 and z is 0.4750

c) The area to the left of z is 0.7291

d) The area to the right of z is 0.1314

e) The area to the left of z is 0.6700

f) The area to the right of z is 0.3300

9. Given that z is a standard random variable, find z for each situation.

a) The area between – z and z is 0.9030

b) The area between – z and z is 0.2052

10. The average stock price for companies making up the S&P is $30, and the standard deviation is $8.20. Assume the stock prices are normally distributed.

a) What is the probability that a company will have a stock of at least $40?

b) What is the probability that a company will have a stock price no higher than $20?

c) How high does a stock price have to be to put a company in the top 10%?