. Birth weight in the U.S.A. are normally distributed with a mean of 3560 gram a

Question

. Birth weight in the U.S.A. are normally distributed with a mean of 3560 gram and a standard deviation of 435 gram.

a. Find the probability that any randomly selected baby has weight less than 2960 grams

b. Find the probability that any randomly selected baby has weight no less than 3100 grams

c. Find the probability that any randomly selected baby has weight between 2960 grams and 3000 grams

d. In a sample of 30 randomly selected babies, what is the probability that their average weights is no more than 3300 grams e. If American Medical Association consider that the lightest 5% babies needs the special observation, find the cut off weight of babies who need special observation.

Explanation / Answer

mean = 3560 , s = 435

a) P( X < 2960)

z = ( x - mean)/ s

= ( 2960 - 3560) / 435

= -1.38

Now, we need to find P(z < -1.38)

P(X < 2960) = P(z < -1.38) = .0839

b)

P( X >3100)

z = ( x - mean)/ s

= ( 3100 - 3560) / 435

= -1.06

Now, we need to find P(z >-1.06)

P(X>3100) = P(z >-1.06) = .8549

c) P(2960 < X < 3000)

P( X < 2960)

z = ( x - mean)/ s

= ( 2960 - 3560) / 435

= -1.38

P( X < 3000)

z = ( x - mean)/ s

= ( 3000 - 3560) / 435

= -1.29

P(2960 < x < 3000) = P( -1.38 < z < -1.29) = 0.0151

d)

n =30

P( X < 3300)

z = ( x - mean)/ (s/sqrt(n))

= ( 3300 - 3560) / (435/sqrt(30))

= -7.05

Now, we need to find P( z < -7.05)

P( x < 3300) = P( Z < -7.05) = 0.0005

e) z value for 5% = -1.645

x bar = mean+ z * s

= 3560 - 1.645 * 435

= 2844.489

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