A recent survey by the American Automobile Association revealed that 80% of teen

Question

A recent survey by the American Automobile Association revealed that 80% of teenage girls text while driving. You have been hired to do a safety presentation to a high school class of 100 teenage girls. a). What is the probability that at least 85 of these girls text while driving? b). What is the probability that fewer than 70 of these girls text while driving? A recent survey by the American Automobile Association revealed that 80% of teenage girls text while driving. You have been hired to do a safety presentation to a high school class of 100 teenage girls. a). What is the probability that at least 85 of these girls text while driving? b). What is the probability that fewer than 70 of these girls text while driving? a). What is the probability that at least 85 of these girls text while driving? b). What is the probability that fewer than 70 of these girls text while driving?

Explanation / Answer

This problem is a binomial experiment. It has only two outcomes, yes or no.

n = 100

p =0.80

q = 1 –p = 0.20

Pdf = nCx pn-x qx

Cdf = P(X x)

a)P(x 85) = 1 – P(x 84)

Using excel function binomdist(number of success, n , probability, cumulative(TRUE or FALSE)

In this case, =1-binomdist(84,100,0.8,TRUE)

P(x 85) = 1 – P(x 84) = 0.128506

b) P( x < 70) = P(x 70) – P(x=70)

excel function =BINOMDIST(70,100,0.8,TRUE)-BINOMDIST(70,100,0.8,FALSE)

P( x < 70) = P(x 70) – P(x=70) = 0.006059

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