Question

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.

Answer 1

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.