Question

1. Suppose that the actual weight of 64-ounce bags of sugar have a skewed distribution with a mean of 65.0 ounces and a standard deviation of 0.5. Weights will be measured for a random sample of 32 bags and the sample mean will be computed.

1. What distribution will be sample mean have in this setting?
   1. Exact normal distribution
   2. Approximate t distribution
   3. Approximate normal distribution
   4. Standard normal distribution
2. What is the probability that the sample mean weight of the 32 bags of sugar is between 64.9 ounces and 65.2 ounces?

Answer 1

Solution :

Given that ,

mean = = 65

standard deviation = = 0.5

Approximate normal distribution (Standard normal distribution)

n = 32

sample distribution of sample mean is ,

=

= 65

sampling distribution of standard deviation

=  / n = 0.5/ 32=0.088

= 0.088

P(64.9< x < 65.2) = P[(64.9-65) /0.088 < (x - ) / < (65.2-65) /0.088 )]

= P( -1.14< Z < 2.27)

= P(Z <2.27 ) - P(Z < -1.14)

Using z table   

= 0.9884 - 0.1271

probability= 0.8613