The average birth weight for babies at a certain hospital is 6.78 pounds weight

Question

The average birth weight for babies at a certain hospital is 6.78 pounds weight a standard deviation of 0.45 pounds. Assume that the distribution of birth weights is normal. a) What is tine probability that a baby born at this hospital has a weight between 6.00 and 7.00 pounds? b) What percentage of babies born weigh at least 3.00 pounds?. c) Unusually small babies are given special attention. If the hospital defines "unusually small" as having a birth weight below the fifth percentile, then what is the maximum birth weight that ments special attention?

Explanation / Answer

Answer to all the parts of Qn:

Mean = 6.78
Stdev = .45

a. P(6<X<7) = P( 6-6.78 / .45 <Z< 7-6.78 /.45)
= P(-1.73<.49)
=.6879-.0409
=.647

b. P(X>8) = P(Z> 1.22/.45) = P(Z>2.711) = 1-.9966 = .0034 or .34%
c. P(X<a) = .05, So, the Z for this -1.645

So,

a= -1.645*.45 +6.78
= 6.04

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