It is estimated that 70% of a grapefruit crop is good; the other 30% have rotten

Question

It is estimated that 70% of a grapefruit crop is good; the other 30% have rotten centers that cannot be detected unless the grapefruit are cut open. The grapefruit are sold in sacks of 11. Let r be the number of good grapefruit in a sack.

a. What is the probability of getting no more than one bad grapefruit in a sack? (Round your answer to three decimal places.)

b. What is the probability of getting at least one good grapefruit? (Round your answer to three decimal places.)

c. What is the expected number of good grapefruit in a sack? (Round your answer to one decimal place.)

d. What is the standard deviation of the r probability distribution? (Round your answer to two decimal places.)

Explanation / Answer

a. What is the probability of getting no more than one bad grapefruit in a sack? (Round your answer to three decimal places.)

P(x<=1 )

P(x=0) = 11C0 * 0.70^0 * 0.30^11-0 = 0.000001771

P(x=1) = 11C1 * 0.70^1 * 0.30^11-1 =0.000045467

P( x <= 1) = 0.000047238

b. What is the probability of getting at least one good grapefruit?

P( x >=1 ) = 1 - 0.000047238 = 0.9999527613

c)

expected number good = 0.70 * 11 = 7.7

SD = srqt ( 0.70 * 0.30 * 11 ) = 1.52

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.