Question

A manufacturing company measures the weight of boxes before shipping them to the customers. The box weights have a population mean and standard deviation of 86 lbs. and 16 lbs. respectively.

a. Based on a sample size of 64 boxes, the probability that the
average weight of the boxes will exceed 90.3 lbs. is .
*Use only the appropriate formula and/or statistical
table in your textbook to answer this question. Report your answer
to 4 decimal places, using conventional rounding
rules.*

b. Based on a sample size of 64 boxes, the probability that the
average weight of the boxes will be between 82.3 and 84.5 lbs. is .
*Use only the appropriate formula and/or statistical
table in your textbook to answer this question. Report your answer
to 4 decimal places, using conventional rounding
rules.*

c. Based on a sample size of 64 boxes, the probability that the
average weight of the boxes will be less than 87.7 lbs. is .
*Use only the appropriate formula and/or statistical
table in your textbook to answer this question. Report your answer
to 4 decimal places, using conventional rounding
rules.*

d. If random samples of 64 boxes are repeatedly drawn from this
population and the mean number of ounces in each sample is
recorded, 82.9% of the sample means should be
above pounds. *Use only the appropriate
formula and/or statistical table in your textbook to answer this
question. Report your answer to 2 decimal places, using
conventional rounding rules.*

Answer #1

a) P( > 90.3)

= P(( - )/() > (90.3 - )/())

= P(Z > (90.3 - 86)/(16/))

= P(Z > 2.15)

= 1 - P(Z < 2.15)

= 1 - 0.9842

= 0.0158

b) P(82.3 < < 84.5)

= P((82.3 - )/() < ( - )/() < (84.5 - )/())

= P((82.3 - 86)/(16/) < Z < (84.5 - 86)/(16/))

= P(-1.85 < Z < -0.75)

= P(Z < -0.75) - P(Z < -1.85)

= 0.2266 - 0.0322

= 0.1944

c) P( < 87.7)

= P(( - )/() < (87.7 - )/())

= P(Z < (87.7 - 86)/(16/))

= P(Z < 0.85)

= 0.8023

d) P( > x) = 0.829

or, P(( - )/() > (x - )/()) = 0.829

or, P(Z > (x - 86)/(16/)) = 0.829

or, P(Z < (x - 86)/(16/)) = 0.171

or, (x - 86)/(16/) = -0.95

or, x = -0.95 * (16/) + 86

or, x = 84.10

The weights of bottles of Meguiar's Gold Class Car Wash Shampoo
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Part 1
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