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“According to a Pew Research Study conducted in 2016, 42% of senior citizens in

ID: 3061446 • Letter: #

Question

“According to a Pew Research Study conducted in 2016, 42% of senior citizens in the US have smartphones. 550 seniors have registered for classes at a local community center. The center director is going to ask each senior whether he or she owns a smartphone.”

5. For the binomial experiment described above:

a. Identify n and p (be sure to label which is which)

b. Find the mean (or expected value) for the experiment

c. Find the standard deviation for the experiment

d. Find the probability that more than 250 of the seniors asked do own a smartphone.

Explanation / Answer

a)

n = 550 , p= 0.42

b)
mean = np = 0.42 * 550 = 231

c)
std.dev. = sqrt ( npq)
= sqrt ( 550 * 0.42 * 0.58)
= 11.5749

d)
P(X > 250) = nCx * p^x * q^(n-x)
= 1 - p(X < =250)
= 1 - 0.9536 [by using excel formula =BINOM.DIST(250, 550,0.42,TRUE)]
= 0.0464