Reference no: EM13842995

1. Consider the following probability density function for the continuous random variable, X.

a. Find h

b. Find P(X > 1)

c. Find P(X =1/2)

2. Given the following CDF, F(x) =

a. Find P(X 1/2)

b. P(-2 < X < 0)

c. P(-1/2 X < 1/2)

3. Suppose the probability of a continuous random variable X, occurring over the range from two to seven, is constant.

a. Draw a picture of the PDF.

b. Find the PDF function,f(x).

C. Find P(3 < X < 6)

4. Suppose Tommy is a delivery driver for Jed's Crispy Pizza Junction. It is known that the time it takes to deliver a pizza has a uniform distribution from twenty minutes to sixty minutes.

a. What is the probability that the time to deliver a pizza is less than thirty-five minutes?

b. If the time to deliver the pizza is longer than fifty minutes, the customer will receive $5.00 off the price of the pizza. What is the probability that the customer will receive $5.00 off the price?

5. Suppose Z represents the standard normal random variable. If a value is selected from the standard normal distribution, find the probability that Z is:

a. less than 0

b. between -2.35 and 1.65

c. greater than 1.86

d. greater than -2.15 and less than 1.67

e. less than -1.92 and greater than 2.41

6. Suppose the incubation period for land turtle eggs is normally distributed with a mean of sixty-seven days and standard deviation 7.4 days.

a. Find the probability that a land turtle egg will take at least eighty days to hath.

b. Find the probability that a land turtle egg will take at most fifty-five days to hatch.

c. Find the probability that a land turtle egg will take between fifty and eight-five days to hatch.

d. Find the length of time such that 85% of the land turtle eggs will have hatched by then.

e. Suppose a veterinarian becomes concerned about the health of the land turtle if it takes longer than ninety days to hatch. What is the probability of this happening if the turtle is healthy? Is it likely for this to happen?

f. Find and interpret the 90th percentile.

7. Suppose the length of time of a whale's song is normally distributed with mean 12.5 minutes and standard deviation 2.6 minutes.

a. Find the probability that a whale's song will last more than ten minutes.

b. Find the probability that a whale's song will last between eight and sixteen minutes.

c. Find the probability that a whale's song lasts less than five minutes or longer than twenty minutes.

d. Find the length of time such that only 5% of whale's songs last longer than that.

e. Find the length of time such that only 10% of whale's songs are shorter than that.

8. Let X be the number of minutes after nine o'clock that the Downtown Marcela street subway leaves the station. Assume that the distrubtion of times is approximately normal with mean fifteen minutes and standard deviation five minutes.

a. If a person gets to the subway station at 9:10, what is the probability that the person has missed the Downtown Marcela Street subway?

b. If a person is willing to risk a 15% chance of not making the Downtown Marcela Street subway, what is the maximum number of minutes after nine o'clock that the person can reach the station.

c. What time should the person reach the station to have a 50% chance of catching the Downtown Marcela Street subway?

9. Suppose the random variable X has a normal distribution with a mean of ninety and a standard deviation of six.

a. Find the Quartiles

b Find P30