Bags checked for a certain airline flight have a mean weight of 15 kg with a standard deviation of 5 kg. A random sample of 60 bags is drawn.

a. What is the probability that the sample mean weight is less than 14 kg?

b. Find the 70th percentile of the sample mean weights.

c. How many bags must be sampled so that the probability is 0.01 that the sample mean weight is less than 14 kg?

Answer:

Step 1 of 3:

(a)

In this question, we are asked to find the probability that the sample mean weight is less than .

Mean weight of bag is and standard deviation is kg.

A random sample of bags is drawn.

Let denote the drawn bags.

We need to find

Now the sample size is , which is a large sample.

Hence can be approximately normal distributed.

CLT specifies that , variance and standard deviation

Hence our sample mean and standard deviation is,

= 0.6455

Therefore the score of 14 is

=

=

=

From the z table, the area to the left of is 0.060.

Hence the probability that the sample mean weight is less than is 0.060.