According to a recent article the average number of babies born with significant hearing loss (deafness) is approximately four per 1,000 babies in a healthy baby nursery. The number climbs to an average of 30 per 1,000 babies in an intensive care nursery. Suppose that 1,000 babies from healthy baby nurseries were randomly surveyed. Find the probability that exactly four babies were born deaf

Question
Asked Oct 21, 2019
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According to a recent article the average number of babies born with significant hearing loss (deafness) is approximately four per 1,000 babies in a healthy baby nursery. The number climbs to an average of 30 per 1,000 babies in an intensive care nursery. Suppose that 1,000 babies from healthy baby nurseries were randomly surveyed. Find the probability that exactly four babies were born deaf
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Expert Answer

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Step 1

The probability that exactly for babies were born deaf is obtained below:

From the given information, the average number of babies born with significant hearing loss is approximately four per 1,000 babies calculated as follows

4
P(Hearing lossin healthy babynur sery) =
1,000
0.004
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4 P(Hearing lossin healthy babynur sery) = 1,000 0.004

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Step 2

 The distribution is binomial distribution with sample size (n) 1,000 and probability of success (p) 0.004. That is, X~ Binomial (1,000, 0.004).

The formula for the probability of binomial distribution is,

п
P(X x) p) (1-p)^here x=0,1,2,...,n for 0s ps1
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п P(X x) p) (1-p)^here x=0,1,2,...,n for 0s ps1

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Step 3

The required proba...

(1000
(0.004) (1- 0.004)"
1000-4
P(X=4)
4
(1000
(0.004) (0.996)
996
4
0.1958
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(1000 (0.004) (1- 0.004)" 1000-4 P(X=4) 4 (1000 (0.004) (0.996) 996 4 0.1958

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