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at a computer manufacturing company, the actual size of a particular type of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. a random sample of 12 computer chips is taken. what is the probability that the sample mean will be between 0.99 and 1.01 centimeters? round answers to four decimal places.

1 Answer

4 votes

Answer: 0.2737

Explanation:

(

0.99

<

ˉ

<

1.01

)

=

(

0.99

1

0.1

12

<

<

1.01

1

0.1

12

)

=

P(0.99<

X

ˉ

<1.01)=P(

12

0.1

0.99−1

<Z<

12

0.1

1.01−1

)=

=

(

0.35

<

<

0.35

)

=

(

<

0.35

)

(

<

0.35

)

=

0.2737.

=P(−0.35<Z<0.35)=P(Z<0.35)−P(Z<−0.35)=0.2737.

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