Question

In: Statistics and Probability

The amount filled per container by an automated process follows an approximately normal distribution with a...

The amount filled per container by an automated process follows an approximately normal distribution with a mean of 128.1 ounces and a standard deviation of 0.16 ounces.

a. Draw a sketch of this normal curve using both the x- and z-axes.

b. Find the probability that the amount filled in a container is between 127.0 ounces and 128.0 ounces.

Solutions

Expert Solution

Let X is a random variable shows the amount filled per container. Here X has normal distribution with

(a)

Following is the normal distribution (z-axes):

Following is the normal distribution (x-axes):

(b)

The z-score for X = 127 is

The z-score for X = 128 is

The probability that the amount filled in a container is between 127.0 ounces and 128.0 ounces is

P(127 < X < 128) = P(-0.625 <z < -6.875) = 0.266

orchestra answered 2 years ago
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