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Naddika [18.5K]
3 years ago
8

Heated-treated parts are specified to have a hardness of at least 45 (lower specification limit). Any parts that are below 45 ar

e too soft and have to be heat treated again at great expense. The hardness of heat-treated parts actually produced follows a normal distribution with a mean of 48.5 with a standard deviation of 2. (Note: sketch of the distribution helps the set up your calculation). What is the probability that a part is below the minimum specified hardness

Mathematics
1 answer:
Nataly_w [17]3 years ago
5 0

Answer:

P(X

And we can find this probability using the normal standard table or excel and we got:

P(z

The figure shows the calculation for this case.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the hardness of a population, and for this case we know the distribution for X is given by:

X \sim N(48.5,2)  

Where \mu=48.5 and \sigma=2

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability using the normal standard table or excel and we got:

P(z

The figure shows the calculation for this case.

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