Question 6

The National Center for Health Statistics reported the following data on the number of

children born in individual pregnancies in 1996 and 2006 (The World Almanac, 2010):

Distribution of Paper Currency Prizes

Bill Denomination Number of Bills

$1 520

$5 260

$10 120

$20 70

$50 29

$100 1

Total 1000

1996 2006

Number of Children Frequency Frequency

one child 3,671,455 3,971,276

twins 100,750 137,085

triplets 5,298 6,118

quadruplets 560 355

quintuplets or more 81 67

a. Define a random variable x number of children born in a single pregnancy in 1996

and develop a probability distribution for the random variable. Let x 5 represent

quintuplets or more.

b. Compute the expected value and variance for the number of children born in a single

pregnancy in 1996.

c. Define a random variable y number of children born in a single pregnancy in 2006

and develop a probability distribution for the random variable. Let y 5 represent

quintuplets or more.

d. Compute the expected value and variance for the number of children born in a single

pregnancy in 2006.

e. Do these data support the conclusion that the increased use of fertility drugs by older

women has generated an upward trend in multiple births?

Question 9

Consider a binomial experiment with 2 trials and p 0.4.

a. Compute the probability of 1 success, f(1).

b. Compute f(0).

c. Compute f(2).

d. Find the probability of at least one success.

e. Find the expected value, variance, and standard deviation.

Question 31

The time between arrivals of vehicles at a particular intersection follows an exponential

probability distribution with a mean of 12 seconds.

a. Sketch this exponential probability distribution.

b. What is the probability that the time between vehicle arrivals is 12 seconds or less?

c. What is the probability that the time between vehicle arrivals is 6 seconds or less?

d. What is the probability that there will be 30 or more seconds between arriving

vehicles?