The probability that the sample mean hardness for a random sample of 17 pins is at least 51 is, 0.0110.
What is probability?
Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.
The distribution is normal.
We have to find the probability that the sample mean hardness for a random sample of 17 pins is at least 51.
The probability that sample mean hardness for a sample of 17 pins is at least 51 is calculated as follows:
P(x bar > 51) = 1 - P(x bar ≤ 51)
= 1 - P((x bar - μ)/σ ≤ (51 - 50)/0.437)
= 1 - P(Z ≤ (1/0.0437)
= 1 - P(Z ≤ 2.29)
= 1 - 0.9890
= 0.0110
Hence, the probability is, 0.0110
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