Question

A manufacturing process produces bags of chips whose weight is N(16 oz, 1.5 oz). On a given day, the quality control officer takes a sample of 36 bags and computed the mean weight of these bags. The probability that the sample mean weight is below 16 oz is

Group of answer choices:
A. 0.55
B. 0.45
C. 0.50
D. 0.60

Answer 1

C. 0.50

Explanation:

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable who represent the weight for bags of chips of a population, and for this case we know the distribution for X is given by:

n=16 represent the sample size

`\mu =16` represent the true mean

`\sigma=1.5` represent the population standard deviation

`X \sim N(16,1.5)`

Where
`\mu=16` and
`\sigma=1.5`

And let
`\bar X` represent the sample mean, the distribution for the sample mean is given by:

`\bar X \sim N(\mu,(\sigma)/(√(n)))`

The probability that the sample mean weight is below 16 oz is:

`P(\bar x<16)=P(Z<(16-16)/((1.5)/(√(36))))=P(Z<0)=0.5`

So the best option for this case is 0.5