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. Suppose that this result is true for the current population of women employees. A random sample of 20 women employees is seleceted. Use binomial probabilities table or technology to find the probability that the number of women employees in this sample of 20 who will hold the above opinion in response to the said question is

a. At least 5

b. 1 to 3

c. At most 6

round your answer to four decimal places
in Statistics Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

2 Answers

The binomial expansion of (0.2+0.8)^20 provides terms for all possibilities from all 20 women crying to no women crying. The expansion of the binomial expression has the coefficients 1, 20, 190, 1140, ... 20Cr, ... 190, 20, 1. The corresponding probability factors are 0.2^20, 0.2^19*0.8, 0.2^18*0.8^2, ... 0.2^(20-r)0.8^r, ... 0.2^2*0.8^18, 0.2*0.8^19, 0.8^20. These factors are: all 20 with crying response, 19 crying and 1 not crying, 18 crying and 2 not crying, and so on up to only 2 crying, only 1 crying, none crying.

a. At least 5 crying

This includes all women crying, i.e., we need to sum all the binomial terms from r=0 to 15. This comes to 0.3704.

b. 1 to 3

Sum from r=17 to 19 = 0.4000.

c. At most 6

Sum from 14 to 20=0.9133.

by Top Rated User (982k points)
idk. can i have money?

Related questions

Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
86,974 questions
95,835 answers
24,325 users