Question

Temp A                                                            Temp B

Mean = 101.52                                                Mean = 98.48

Standard deviation = 1.05                              Standard deviation = 0.65

a. Calculate a 95% tolerance interval for Temp A. Round each value to 2 decimal places

b. Calculate a 95% tolerance interval for Temp B. Round each value to 2 decimal places

c. Is there any overlap between the tolerance intervals you calculated in parts (a) and (c) (i.e do they cover any of the same region on a number line – for example, an interval of [1,2] and an interval of [1.5, 3] would have some overlap because both of them cover the region [1.5, 2])? Please answer ‘yes or no’. No need to show work. [1 mark]

d. How much do these tolerance intervals overlap (i.e. what is the percentage overlap – take ((length of overlap)/(length of both intervals together))*100 – for example, ((2-1.5)/(3-1))*100 = 25% overlap)? Show your work. [1 mark]

f. Assume the optimal temperature for production is 100C. Based on your 95% tolerance intervals, which machine should you use to produce the units, and why? List one additional business- related factor that should affect your decision.

Answer 1

a. Calculate a 95% tolerance interval for Temp A. Round each value to 2 decimal places

101.52 - 2*1.05 = 99.42

101.52 + 2*1.05 = 103.62

b. Calculate a 95% tolerance interval for Temp B. Round each value to 2 decimal places

98.48 - 2*0.65 = 97.18

98.48 + 2*0.65 = 99.78

c. Is there any overlap between the tolerance intervals you calculated in parts (a) and (c) (i.e do they cover any of the same region on a number line – for example, an interval of [1,2] and an interval of [1.5, 3] would have some overlap because both of them cover the region [1.5, 2])? Please answer ‘yes or no’. No need to show work. [1 mark]

yes

d. How much do these tolerance intervals overlap (i.e. what is the percentage overlap – take ((length of overlap)/(length of both intervals together))*100 – for example, ((2-1.5)/(3-1))*100 = 25% overlap)? Show your work. [1 mark]

((99.78- 99.42)/(103.62 - 97.18))*100 = 5.59%

f. Assume the optimal temperature for production is 100C. Based on your 95% tolerance intervals, which machine should you use to produce the units, and why? List one additional business- related factor that should affect your decision.

Temp A will be used since it is the only interval that contains 100C.

Cost is the factor.