Central Limit Theorem: The Rockwell hardness of certain metal pins is known to have a mean of 50 and a stan- dard deviation of 1.5 (Round your answers to 4 decimal places). (a) If the distribution of all such pin hardness measurements is known to be normal, what is the probability that the mean hardness for a random sample of 9 pins is at least 52? (a). (b) What is the approximate probability that the mean hard- a random sample of 40 pins is at least 52? ness (b).

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**Central Limit Theorem:** The Rockwell hardness of certain metal pins is known to have a mean of 50 and a standard deviation of 1.5 *(Round your answers to 4 decimal places).*

(a) If the distribution of all such pin hardness measurements is known to be normal, what is the probability that the mean hardness for a random sample of 9 pins is at least 52?

(a) ____________

(b) What is the approximate probability that the mean hardness in a random sample of 40 pins is at least 52?

(b) ____________

*Image description:* The image contains a picture of a hardness testing machine used to measure the Rockwell hardness of metal pins.
Transcribed Image Text:**Central Limit Theorem:** The Rockwell hardness of certain metal pins is known to have a mean of 50 and a standard deviation of 1.5 *(Round your answers to 4 decimal places).* (a) If the distribution of all such pin hardness measurements is known to be normal, what is the probability that the mean hardness for a random sample of 9 pins is at least 52? (a) ____________ (b) What is the approximate probability that the mean hardness in a random sample of 40 pins is at least 52? (b) ____________ *Image description:* The image contains a picture of a hardness testing machine used to measure the Rockwell hardness of metal pins.
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