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Question

The probability that a call to an emergency help line is answered in less than 15 seconds is 0.85. Assume that all calls are independent. (a) What is the probability that exactly 7 of 10 calls are answered within 15 seconds? (b) What is the probability that at least 16 of 20 calls are answered in less than 15 seconds? (c) For 50 calls, what is the mean number of calls that are answered in less than 15 seconds? (d) Repeat parts (a)–(c) using the normal approximation.

Solution

VerifiedStep 1

1 of 8Given:

$p=0.85$

Definition binomial probability:

$P(X=k)=_nC_k\cdot p^k\cdot (1-p)^{n-k}=\dfrac{n!}{k!(n-k)!}\cdot p^k\cdot (1-p)^{n-k}$

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