Question

At intel, the actual size of the processor chip has a mean of 1 cm with a standard deviation of 0. 2 cm. Random samples, each consisting of 35 processor chips, are taken. Above what value does 3. 5% of the sample means fall?.

Answer 1

3.5% of the sample means fall above 1.06 cm.

Z score

z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

$z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\\mu=mean=1\ cm,\sigma=standard\ deviation=0.2\ cm,x=raw\ score,n=sample$

From the normal distribution table:

P(z > z*) = 3.5%

1 - P(z < z*) = 3.5%

P(z < z*) = 96.5%

z* = 1.81

Using the z score formula:

$1.81=\frac{x-1}{0.2/\sqrt{35} } \\\\x=1.06$

3.5% of the sample means fall above 1.06 cm.

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