Rabbits like to eat the cucumbers in Mimi’s garden. There are 10 cucumbers in he

Question

Rabbits like to eat the cucumbers in Mimi’s garden. There are 10 cucumbers in her garden which will be ready to harvest in about 10 days. Based on her experience, the probability of a cucumber being eaten by the rabbits before harvest is 0.30.

(a) Let X be the number of cucumbers that Mimi harvests (that is, the number of cucumbers not eaten by rabbits). As we know, the distribution of X is a binomial probability distribution. What is the number of trials (n), probability of successes (p) and probability of failures (q), respectively?

(b) Find the probability that Mimi harvests at least 8 of the 10 cucumbers. (round the answer to 3 decimal places) Show all work. Just the answer, without supporting work, will receive no credit.

Explanation / Answer

Ansswer-

Let X be the number of cucumbers that Mimi harvests

a) number of trials (n)=10

probability of successes (p)=0.30

probability of failures(q=1-p)=1-0.30=0.70

Probability density function of binomial distribution is given by

P(X=x) = nCx Px (1-P)n-x x=0,1,2......... >>>>>>>>>> (1)

b)

  probability that Mimi harvests at least 8 of the 10 cucumbers (i.e at least : >=)

i.e P(X>= 8)

= P(x=8)+P(x=9) +P(X=10)

=10C8 (0.30)8 (0.70)2    +10C9 (0.30)9 (0.70)1 +10C10 (0.30)10 (0.70)0

= 0.001446701 + 0.00013 77 +0.00000590

=0.00159

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Best of luck :)

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