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Art [367]
3 years ago
7

The diameters of ball bearings are distributed normally. The mean diameter is 87 millimeters and the standard deviation is 6 mil

limeters. Find the probability that the diameter of a selected bearing is greater than 84 millimeters. Round your answer to four decimal places.
Mathematics
1 answer:
devlian [24]3 years ago
7 0

Answer:

69.14% probability that the diameter of a selected bearing is greater than 84 millimeters

Step-by-step explanation:

According to the Question,

Given That, The diameters of ball bearings are distributed normally. The mean diameter is 87 millimeters and the standard deviation is 6 millimeters. Find the probability that the diameter of a selected bearing is greater than 84 millimeters.

  • In a set with mean and standard deviation, the Z score of a measure X is given by Z = (X-μ)/σ

we have μ=87 , σ=6 & X=84

  • Find the probability that the diameter of a selected bearing is greater than 84 millimeters

This is 1 subtracted by the p-value of Z when X = 84.

So, Z = (84-87)/6

Z = -3/6

Z = -0.5 has a p-value of 0.30854.

⇒1 - 0.30854 = 0.69146

  • 0.69146 = 69.14% probability that the diameter of a selected bearing is greater than 84 millimeters.

Note- (The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X)

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Answer: x=-2

Step-by-step explanation:

Here is the step-by-step solving.

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7 0
3 years ago
Read 2 more answers
Let N be the universal set and A, B, C, D be its subsets given by A={x:xisaevennaturalnumber},B={x:xNandxisamultipleof3} C={x:x
Svet_ta [14]

Answer:

A^{'} = {1,3,5,7,9,....}

B^{'} = {1,2,4,5,7,8,10,11,13,14......}

C^{'} = {1,2,3,4,5}

D^{'} = {10,11,12,13,14,15,......}

Step-by-step explanation:

Solution:

It is given that, Universal set is the set of all Natural Numbers.

and

Set A, Set B, Set  C, Set D are subsets of Universal set.

A = {x:x is even natural numbers} = {2,4,6,8,10,.....}

B = {x:x ∈ N and x is a multiple of 3} = {3,6,9,12,15,....}

C = {x:x∈ N and x < 5} = {6,7,8,9,10,.....}

D = {x:x ∈ N and x > 10} = {1,2,3,4,5,6,7,8,9}

U = {1,2,3,4,5,6,7,8,9,10,11,........}

Complements:

A^{'} = U-A = {1,2,3,4,5,6,7,8,9,10,11,........} - {2,4,6,8,10,.....}

A^{'} = {1,3,5,7,9,....}

B^{'} = U-B =  {1,2,3,4,5,6,7,8,9,10,11,........} - {3,6,9,12,15,....}

B^{'} = {1,2,4,5,7,8,10,11,13,14......}

C^{'} = U-C = {1,2,3,4,5,6,7,8,9,10,11,........} - {6,7,8,9,10,.....}

C^{'} = {1,2,3,4,5}

D^{'} = {1,2,3,4,5,6,7,8,9,10,11,........} - {1,2,3,4,5,6,7,8,9}

D^{'} = {10,11,12,13,14,15,......}

8 0
3 years ago
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