A manufacturer knows that their items have a normally distributed length, with a mean of 10.2 inches, and standard deviation of 1.8 inches.

Question

A manufacturer knows that their items have a normally distributed length, with a mean of 10.2 inches, and standard deviation of 1.8 inches. If 25 items are chosen at random, what is the probability that their mean length is less than 9.8 inche

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Thanh Hà 4 years 2021-08-03T11:57:04+00:00 1 Answers 31 views 0

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  1. thugiang
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    2021-08-03T11:58:52+00:00
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    Answer:

    P [ X ≤  9.8 ]  = 0.1335

    Step-by-step explanation:

    P [ X ≤  9.8 ]  =  [ ( 9.8  – 10.2 )/1.8√25 ]

    P [ X ≤  9.8 ]  =  – 0.4*5/1.8

    P [ X ≤  9.8 ]  = – 2 / 1.8

    P [ X ≤  9.8 ]  =  – 1.11

    From z- table we get:  α  =  0.1335

    P [ X ≤  9.8 ]  = 0.1335   or   P [ X ≤  9.8 ]  = 0.1335

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