For each of the following random processes, determine whether it describes a binomial random variable. If it does, identify what n and p are. If it isn’t, briefly say why. Recall that binomial random variables count how many times a “success” happens across n trials with only two outcomes (“success” with probability p and “failure” otherwise). (If you think it is binomial but it isn’t clear what n or p is, you may want to reconsider whether it’s actually binomial.) a) Count the number of sixes in 10 dice rolls. b) Worldwide, the proportion of babies who are boys is 0.51. We randomly sample 100 babies born and count the number of boys. c) Roll a die until you get 5 sixes and count the number of rolls required.
For each of the following random processes, determine whether it describes a
binomial random variable. If it does, identify what n and p are. If it isn’t, briefly say
why. Recall that binomial random variables count how many times a “success”
happens across n trials with only two outcomes (“success” with probability p and
“failure” otherwise). (If you think it is binomial but it isn’t clear what n or p is, you
may want to reconsider whether it’s actually binomial.)
a) Count the number of sixes in 10 dice rolls.
b) Worldwide, the proportion of babies who are boys is 0.51. We randomly sample
100 babies born and count the number of boys.
c) Roll a die until you get 5 sixes and count the number of rolls required.
d) Sample 50 students who have taken Stat 150 and record the final grade in the
course for each.
e) Suppose 30% of students at a large university take Intro Stats. Randomly sample
75 students from the university and count the number who have taken Intro Stats.
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