1. At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 cm and a standard deviation of 0.1 cm. A random sample of 12 computer chips is taken. What is the standard error for the sample mean?2. At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 cm and a standard deviation of 0.1 cm. 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 cm?3. At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 cm and a standard deviation of 0.1 cm. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be below 0.95 cm?4. At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 cm and a standard deviation of 0.1 cm. A random sample of 12 computer chips is taken. Above what value do 2.5% of the sample means fall?

The 4 answers are given below:

0.1cm,  0.1 probability,  0.25 probability,  1.095cm

Step-by-step explanation:

QUESTION HEAD: At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1cm and standard deviation of 0.1cm. A random sample of 12 computer chips is taken.

(A) What is the standard error for the sample mean?

(B) What is the probability that the sample mean will be between 0.99 and 1.01cm?

(C) What is the probability that the sample mean will be below 0.95cm?

(D) Above what value do 2.5% of the sample means fall?

ANSWERS:

(A) The standard error for the sample mean is 0.1cm

(B) [0.99, 1.01]cm?

The mean length is 1cm and S.E. is 0.1cm, hence all lengths fall into the following range: [0.9 - 1.1]

0.99 - 0.9 = 0.09

1.1 - 1.01 = 0.09

0.09 + 0.09 = 0.18

1.1 - 0.9 = 0.2

0.2 - 0.18 = 0.02  This is the fraction of 0.2 that the length bracket in the question occupies. So 0.02/0.2 = 0.1

Hence the probability that the sample mean will be between 0.99 and 1.01cm is 0.1 (which translates to a 10% probability/chance)

(C) The probability that the sample mean will be below 0.95 is:

0.95 - 0.9 = 0.05

0.05/0.2 = 0.25 (which translates to a 25% chance of occurrence)

(D) Above what value do 2.5% of the sample means fall?

Here, you're looking for the value of the mean which serves as the lower limit for the top 2.5% of sample mean values.

2.5% of 0.2 = 0.025 × 0.2 = 0.005

Subtract this from the highest possible mean value:

1.1 - 0.005 = 1.095

So, above 1.095 is where 2.5% of the sample means fall

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