Question

A company finds that one out of four employees will be late to work on a given day. If this company has 41 employees, find the probabilities that the following number of people will get to work on time. (Round your answers to 4 decimal places.) (a) Exactly 31 workers or exactly 35 workers. (b) At least 26 workers but fewer than 34 workers. (c) More than 24 workers but at most 36 workers. The manager of Toy World knows that the probability an electronic game will be returned to the store is 0.23. If 57 games are sold in a given week, determine the probabilities of the following events. (Round your answers to four decimal places.) (a) No more than 14 games will be returned. (b) At least 10 games will be returned. (c) More than 7 games but fewer than 16 games will be returned.

Answer 1

dear student, please post one type of question one at a time.

1) the probability that the employee will be on time =

-= 0.75

the number of employees = 41.

a) The probability that the 31 workers or 35 workers will be on time.

P(X = 31) =31 C(0.75)31(1-0.75)41-31-0, 14:32

P(X-35) = C(0.75)35(1-0.75)41-31-0.0465

The probability that the 31 workers or 35 workers will be on time = P(X=31) + P(X=35) = 0.1432+0.0465 = 0.1897

b) the probability that the employee have At least 26 workers but less than 34 worker =

P26 < X < 34) P(X < 34)-P(X < 26)

P(X < 34) Σ il C(0.75)"(1-075)41-r-0.8395

25 P(X < 26) Σ "C(0.75)"(1-0.75)41-r-0.0333

P(26 < X < 34) 0.8395-0.0333-0.8062

c) the probability that the employee has more than 24 but at most 36

P(24 < X < 36)- P(X <36) - P(X < 24)

36 P(X < 36) 41 〉· 'C(0.75)"(1-075)41-r-0.9868

24 7541-:r P(X < 24) 41 〉·' "C(0.75)"(1-0.75)41一一0.0152

P(24 < X < 36) 0.9868-0.0152-0.9716