Question

Without using Excel (in other words - long hand) A box contains 100 thermometers, of which 10 are defective. You reach in and randomly take 5 thermometers from the box all at once. Let X be the number of non-defective thermometers in your selection. (a) What is the probability that all of the five thermometers are non-defective (that is, that X = 5)? (b) What is the probability that at least 2 of the five thermometers are non-defective? (c) What is the name of the probability distribution for X?

Answer #1

n = 5

non defective, k = 90

total , N = 100

it is hypergeometric distribution | |

and probability is given by | |

P(X=x) =C(k,x)*C(N-k,n-x)/C(N,n) |

A) P(X=5)= C(90,5)*C (10,0)/C(100,5) = 0.5838

B) P(X=0)= C(90,0)*C (10,5)/C(100,5) = 0.0000

P(X=1)= C(90,1)*C (10,4)/C(100,5) = 0.0003

P(X≥2) = 1- P(X=0) - P(x=1) =1 - 0.000 - 0.0003 =
**0.9997**

C) Hypergeometric Distribution

please revert for doubts and |

please UPVOTE the solution |

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