The breaking strength of a rivet has a mean of 10,000 psi and a standard deviation of 714.2857 psi. What is the probability that the sample mean breaking strength for a random sample of 49 rivets is between 9,832 and 10,200?

And we can use the normal standard distribution table or excel and we can  find the probability with this difference:

Then the probability that the sample mean breaking strength for a random sample of 49 rivets is between 9,832 and 10,200 is 0.9251

Step-by-step explanation:

For this case we have the following info given:

represent the mean

represent the deviation

represent the sample size selected

For this case since the sample size is large enough n>30 we have enough evidence to use the central llmit theorem and the distribution for the sample mena would be given by:

And we want to find the following probability:

And we can use the z score formula given by:

And if we use the z score formula for the limits  given we got:

And we can use the normal standard distribution table or excel and we can  find the probability with this difference:

Then the probability that the sample mean breaking strength for a random sample of 49 rivets is between 9,832 and 10,200 is 0.9251

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