Mathematics Homework Help

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?