The Screw Right Company claims their 3/4 inch screws are within ±0.23 of the cla

Question

The Screw Right Company claims their 3/4 inch screws are within ±0.23 of the claimed mean diameter of 0.750 inches with a standard deviation of 0.115 inches. The following data were recorded.

The screws were randomly selected from the local home repair store.

(a) Find the mean diameter and standard deviation for the sample. (Round your answers to three decimal places.)

(b) Find the probability that 50 randomly selected screws will be within the stated tolerance levels. (Round your answer to four decimal places.)
????

Is the company's diameter claim plausible?

Yes

I figured out most of it except for part b can someone help please

0.761 0.741 0.739 0.753 0.756 0.726 0.761 0.744 0.760 0.747 0.716 0.746 0.747 0.750 0.754 0.716 0.736 0.744 0.740 0.751 0.752 0.757 0.762 0.753 0.770 0.760 0.733 0.751 0.750 0.757 0.723 0.761 0.747 0.764 0.762 0.767 0.763 0.766 0.739 0.734 0.748 0.738 0.746 0.735 0.745 0.729 0.732 0.770 0.754 0.749

Explanation / Answer

(B)
xbar = 0.7481
SE = 0.115/sqrt(50) = 0.0163
here we need to find the probability such that the diameter falls between the limit of 0.75 - 0.23 = 0.52 and 0.75+0.23 = 0.98

P(0.52 < X < 0.98) = P((0.52-0.7481)/0.0163 < z < (0.98-0.7481)/0.0163) = P(-13.99 < z < 14.23) = 1

Hence the probability is 1.

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