In a poll, men and women were asked, “When someone yelled or snapped at you at w

Question

In a poll, men and women were asked, “When someone yelled or snapped at you at work, how did you want to respond?” Twenty percent of the women in the survey said that they felt like crying (Time, April 4, 2011). Suppose that this result is true for the current population of women employees. A random sample of 21 women employees is selected. Use the binomial probabilities table or technology to find the probability that the number of women employees in this sample of 21 who will hold the above opinion in response to the said question is

a. at least 5

Round your answer to four decimal places.

b. 2 to 4

Round your answer to four decimal places.

c. at most 6

Round your answer to four decimal places.

Explanation / Answer

Here p = 0.2, n = 21

a)
P(X >= 5)
= 1 - P(X <= 4)

In order to find the probability P(X <= 4) we use the excel formula =BINOM.DIST(4,21,0.2,TRUE)
P(X >= 5) = 1 - 0.5860 = 0.41399

b)
P(2 to 4) = P(2 <= X <= 4) (both 2 and 4 are included)
= P(X <= 4) - P(X <= 1)
= 0.5860 - 0.0576
= 0.5284

Excel formulas for this are P(X <= 4) =BINOM.DIST(4,21,0.2,TRUE) and P(X <= 1 ) =BINOM.DIST(1,21,0.2,TRUE)

c)
P(at most 6) = P(X <= 6) = 0.8915
Excel formula for P(X <= 6) =BINOM.DIST(6,21,0.2,TRUE)

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