Suppose Mom\'s Friendly Robot company produces bending units whose heights are n

Question

Suppose Mom's Friendly Robot company produces bending units whose heights are normally distributed with a mean of 66 inches and a standard deviation of 4 inches. (a) Find the probability that a randomly chosen bending unit is between 60 and 72 inches tall. (b) Find the probability that a randomly chosen bending unit is less than 58 inches tall or greater than 70 inches tall? (c) Find the height in whole inches that contains at least 9-5% of all of the heights of all bending units. (d) Suppose Mom is tired of bending units being taller than her. She decides that she is going to adjust their average height, mu, such that 99% of all bending units are shorter than her height of 70 inches. What is the average height mu that she should use?

Explanation / Answer

mean = 66 , s= 4

a) P(60 < X < 72)

P( X < 60)

z = ( x - mean) /s

= (60-60)/4

= 0

P(X < 72)

z = ( x -mean) / s

= ( 72 -60) / 4

= 3

P(60 < X < 72) = P( 0 < z < 3) = 0.4987

b)

P( X < 58 )

z = (x -mean) / s

= ( 58 - 60) /4

= -0.5

we need to find p(z < -0.5)

P(X < 68) = p(z < -0.5) = 0.3085

P( X > 70 )

z = (x -mean) / s

= ( 70 - 60) /4

= 2.5

we need to find p(z > 2.5)

P(X >70) = p(z >2.5) = 0.0062

c)

z value for 95% = 1.645

x bar = mean + z * s

= 60 + 1.645 * 4

= 66.58

d) z value at 99% = -2.326

mean = x - z*s

= 70 - ( -2.326 * 4)

= 79.305

=

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