The length of a screw produced by a machine is normally distributed with a mean of 0.75 inches and a standard deviation of 0.01
inches. what percent of screws are between 0.72 and 0.78 inches? (1 point 68% 75% 99.7% 100%
2 answers:
Answer: There is 99.7% of screws are between 0.72 and 0.78 inches.
Step-by-step explanation:
Since we have given that
Mean = 0.75 inches
Standard deviation = 0.01 inches
Since the length of a screw produced by a machine is normally distributed.
So, We need to find the percent of screws are between 0.72 and 0.78 inches.
Since we have that
![P(0.72](https://tex.z-dn.net/?f=P%280.72%3CX%3C0.78%29)
And we know that
![z=\frac{X-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7BX-%5Cmu%7D%7B%5Csigma%7D)
So, it becomes,
![P(\frac{0.72-0.75}{0.01}](https://tex.z-dn.net/?f=P%28%5Cfrac%7B0.72-0.75%7D%7B0.01%7D%3Cz%3C%5Cfrac%7B0.78-0.75%7D%7B0.01%7D%29%5C%5C%5C%5C%3DP%28-3%3Cz%3C3%29%5C%5C%5C%5C%3D2%5Ctimes%20P%280%3Cz%3C3%29%5C%5C%5C%5C%3D2%5Ctimes%200.49865%5C%5C%5C%5C%3D0.9973%5C%5C%5C%5C%3D0.9973%5Ctimes%20100%5C%5C%5C%5C%3D99.73%5C%25)
Hence, there is 99.7% of screws are between 0.72 and 0.78 inches.
99.7%
You can use normalCdf(.72,.78,.75,.01) to find the answer or if you standardize your numbers (z scores) normalCdf(-3,3,0,1).
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