Question

Bags checked for a certain airline flight have a mean weight of 15 kg with a standard deviation of 7 kg. A random sample of 60 bags is drawn.

How many bags must be sampled so that the probability is 0.01 that the sample mean weight is less than 14 kg? Round the answer to the next largest whole number.

Answer 1

Let the required sample size be n.

P(X < A) = P(Z < (A - )/)

= = 15 kg

= =

P( < 14) = 0.01

P(Z < (14 - 15)/()) = 0.01

Take Z value corresponding to 0.01 from standard normal distribution table

-1/ = -2.326

/ 7 = 2.326

= 16.31

n = 266 (rounded up)