# Solve these problems using excel

Question 6 The National Center for Health Statistics reported the following data on the number ofchildren born in individual pregnancies in 1996 and 2006 (The World Almanac, 2010):Distribution of Paper Currency PrizesBill Denomination Number of Bills\$1 520\$5 260\$10 120\$20 70\$50 29\$100 1Total 10001996 2006Number of Children Frequency Frequencyone child 3,671,455 3,971,276twins 100,750 137,085triplets 5,298 6,118quadruplets 560 355quintuplets or more 81 67a. Define a random variable x number of children born in a single pregnancy in 1996and develop a probability distribution for the random variable. Let x 5 representquintuplets or more.b. Compute the expected value and variance for the number of children born in a singlepregnancy in 1996.c. Define a random variable y number of children born in a single pregnancy in 2006and develop a probability distribution for the random variable. Let y 5 representquintuplets or more.d. Compute the expected value and variance for the number of children born in a singlepregnancy in 2006.e. Do these data support the conclusion that the increased use of fertility drugs by olderwomen 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 exponentialprobability 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 arrivingvehicles?

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