4 What if you selected a sample of 50 infants from the above

4. What if you selected a sample of 50 infants from the above example: a. What is the standard error of the mean? b. What proportion will be between 3000 and 3500 grams? c. What proportion will be less than 2500 grams? d. What proportion will be over 5000 grams? e. What proportion will be less than 3380 grams? f. What is the 90% confidence interval of µ? g. What is the 98% confidence interval or µ

Solution

µ= 3380 g and = 500 g.

n =50

a) std error of mean = 500/rt 50

= 70.711

b) P(3000<x<3500) = P(-380/70.711<z<120./70.711)

= P(-5.37<z<1.69)

= 0.9535

c) P(X<2500) = 1

d) P(X>5000) = P(Z>1120/70.711)=0.00

e) P(X<3380) = 0.50

f) 90% conf interval = Mean+ or - 1.645(70.711)

=(3380-116.3196, 3380+116.3196)

= (3263.68, 3496.32)

g) 98% confidence interval z = 2.33

Hence ci=(3215.24, 3544.76)