What is the probability that the average of four babies' weights will be within .6 pounds of the mean; will be between 8.4 and 9.6 pounds

The probability will be "0.7497".

Given:

Mean,

Standard deviation,

Number of babies,

The standard error of sample will be:

→

hence,

→ P(4 babies will be between 8.4 - 9.6 pounds)

Thus the above response is right.  

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Complete question:

Some sources report that the weights of full-term newborn babies in a certain town have a mean of 9 pounds and a standard deviation of 0.6 pounds and are normally distributed.

0.7497

Step-by-step explanation:

Mean = 9

sd = 0.6

n = 4

P(4 babies will be between 8.4 and 9.6 pounds)

P(8.4 ≤ X ≤ 9.6)

Standard error of the sample (S. E) :

S. E = sd/√n

= 0.6 /√4

= 0.6/2

= 0.3

P(8.4 ≤ X ≤ 9.6)= ((P(8.4 - 9) / 0.3) ≤ X ≤ (9.6 - 9)/0.3)

P(8.4 ≤ X ≤ 9.6) = P(-2 ≤ X ≤ 2)

P(Z ≤ 2) - P(Z < - 2)

0.9772 - 0.2275 = 0.7497