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zvonat [6]
3 years ago
13

Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.3. (Round your ans

wers to four decimal places.)
(a) If the distribution is normal, what is the probability that the sample mean hardness for a random sample of 12 pins is at least 51?
Mathematics
1 answer:
Maurinko [17]3 years ago
3 0

Answer:

0.0039 is the probability that the sample mean hardness for a random sample of 12 pins is at least 51.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 50

Standard Deviation, σ = 1.3

Sample size, n = 12

We are given that the distribution of hardness of pins is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

Standard error due to sampling =

=\dfrac{\sigma}{\sqrt{n}} = \dfrac{1.3}{\sqrt{12}} = 0.3753

P(sample mean hardness for a random sample of 12 pins is at least 51)

P( x \geq 51) = P( z \geq \displaystyle\frac{51 - 50}{0.3753}) = P(z \geq 2.6645)

= 1 - P(z < 2.6645)

Calculation the value from standard normal z table, we have,  

P(x \geq 51) = 1 - 0.9961= 0.0039

0.0039 is the probability that the sample mean hardness for a random sample of 12 pins is at least 51.

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