Question

Problem 5. (9 points) It is estimated that 75% of a grapefruit crop is good; the other 25% have rotten centers that cannot be detected until the grapefruit are cut open. The grapefruit are sold in sacks of 10. a. What is the probability of getting at least 9 good grapefruit in a sack? • enter your answer as a percent (5%) or as a real-value (0.05) • if you enter your answer as a percent, you must use a %-sign in your answer your answer must be accurate to the nearest whole percent. b. If you purchase a sack of 10 grapefruit, how many can you expect to be good? • Your answers must be accurate to the nearest hundreth. c. What is the standard deviation of the number of good grapefruit in a sack of 10? • Your answers must be accurate to the nearest hundredth. preview answers

Answer 1

here this is binomial with parameter n=10 and p=0.75

a)

P(X>=9)=1-P(X<=8)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.24 or 24 %

b)

mean E(x)=μ=np=7.5

c)

standard deviation σ=√(np(1-p))=1.37