## Question

SeaScrape Industries manufactures small tethered robotic units used to clean the sides of ships below the water level. If the units are operating properly, power consumption per unit is normally distributed with a mean of 1200 watts per hour, with a standard deviation of 105 watts per hour.

The quality control expert would like to know what proportion of units produced consume more than 1350 watts per hour. What is the Z value associated with 1350 watts per hour?

Z =

Question 2

Refer to the previous SeaScrape Industries question.

Using the z value calculated in the previous question, calculate the proportion of units produced that consume more than 1350 watts per hour?

P(X > 1350) = P(Z > _______) =

Question 3

Refer to the previous SeaScrape Industries question.

The company has decided to reject the top 1% of units in terms of power consumption and re-core the motors hoping to reduce their power consumption and would like to determine the value of wattage consumption that would be used if this standard is adopted. What is the Z-value associated with the cutoff value for wattage would they use to set this standard?

P(Z > Zo ) = 0.01; Zo =

Question 4

Refer to the previous SeaScrape Industries question.

Using the Z value from the previous question calculate a value for wattage used (value of X) that is at the 99th percentile.

P( X > Xo) = 0.01; Xo =

Question 5

Refer to the previous SeaScrape Industries question.

Suppose that a sample of 64 units are selected randomly and tested. What is the Z-value associated with the probability that the mean power consumption of the 64 units will exceed 1220 watts per hour?

P( > 1220) = P( Z > ____________ )

Question 6

Refer to the previous SeaScrape Industries question.

What is the probability that the mean power consumption of the 64 units will exceed 1220 watts per hour?

P( > 1220) =

Question 7

According to the Bureau of Transportation Statistics, in 2004, 82% of all US airline flights arrived within 15 minutes of their scheduled arrival time. What is the Z-value associated with the probability that a simple random sample of 200 flights will have an 84% or better on-time arrival rate?

P ( > 0.84 ) = P ( Z > _______________ )

Question 8

Refer to the US Airline problem above.

What is the probability that the random sample of 200 flights will have an 84% or better on-time arrival rate?

P ( > 0.84 ) =

Question 9

Compute the following:

P ( Z > 1.96 ) =

Question 10

Compute the following:

P ( 0 < Z < 0.84 ) =

Question 11

Compute the following:

P ( Z < -0.75 ) =

Question 12

Compute the following:

P ( Z < 1.35 ) =

Question 13

Use this fact statement for the remainder of the exam.

The useful life of a die used in an injection mold, die-casting process varies from die to die. A simple random sample of nine die lives was taken and recorded below as measured in production days:

4.5 5.1 3.5 5.7 5.9 4.6 5.8 2.9 8.3

a. What is the sample mean?

Question 14

b. What is the die life sample standard deviation?

Question 15

c. What is the standard error of the sample mean?

Question 16

d. What is the point estimate for the population mean?

Question 17

e. To find that 95% confidence interval estimate for the population mean die life in days, the correct critical value (interval coefficient) to use is:

Question 18

f. Report the margin of error (confidence bound) for a 95% confidence interval estimate for the population mean die life in days:

Question 19

g. Report the 95% lower and upper confidence limits for your estimate of the population mean:

Question 20

h. Make a statement to interpret your confidence interval estimate.

Question 21

i. The operations manager has adjusted the pressure of the injection material on all machines and now claims the mean die life is at least 4 production days. Do your previous findings support or refute his claim and why?

## Solution Preview

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1. Z = (1350-1200)/105 = 150/105 = 1.4285714292. P(X > 1350) = P(Z > 1.428571429) = 0.0766...