Question

Some sources report that the weights of full-term newborn babies in a certain town have a mean of 7 pounds and a standard deviation of 0.6 pounds and are normally distributed.

a. What is the probability that one newborn baby will have a weight within 0.6 pounds of the mean is, between 6.4 and 7.6 pounds, or within one standard deviation of the mean?

b. What is the probability that the average of four babies' weights will be within 0.6 pounds of the mean; will be between 6.4 and 7.6 pounds? c. Explain the difference between (a) and (b).

Answer 1

(a) Given that

mean = 7.0 and sd = 0.60

using normalcdf

setting lower = 6.4, upper = 7.6, mean = 7 and sd = 0.60

=normalcdf(6.4,7.6,7,0.6)

= 0.6827

(B)

Given that

mean = 7.0, sample size n = 4 and sd = 0.60

using normalcdf

setting lower = 6.4, upper = 7.6, mean = 7 and sd = 0.60/sqrt(4)

=normalcdf(6.4,7.6,7,0.6/sqrt(4))

= 0.9545

(C) Difference between (a) and (b) is that the probability in part (a) is calculated for single mean whereas the probability in part(b) is calculated for the sample mean

we know that the sample mean is more concentrated around the mean, thats why part(b) probability is greater than the part(a) probability