# A normal distribution has a mean u = 54 and a standard deviation of sigma = 6.a) what is the probability of randomly selecting a score less than x = 51?b) what is the probability of selecting a sample  of n = 4 scores with a mean less than M = 51?c) what is the probability of selecting a sample of n = 36 scores with a mean less than M = 51?

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A normal distribution has a mean u = 54 and a standard deviation of sigma = 6.

a) what is the probability of randomly selecting a score less than x = 51?

b) what is the probability of selecting a sample  of n = 4 scores with a mean less than M = 51?

c) what is the probability of selecting a sample of n = 36 scores with a mean less than M = 51?

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Step 1

a)

The probability of randomly selecting a score less than x = 51 is,

Thus, the probability of randomly selecting a score less than x = 51 is 0.3085.

Step 2

(b)

The probability of selecting a sample of n = 4 scores with a mean less than M = 51 is,

Thus, the probability of selecting a sample of n=4 with a mean less than M=51 is 0.1587.s

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