A paint manufacturer wants to determine the average drying time of a new interior wall paint. For n = 50 test areas of equal size he obtained a sample mean drying time of ¯x = 63.3 minutes and a sample standard deviation of s = 8.4 minutes. (a) (5 points) Construct the 95% confidence interval for the true mean µ. (b) (5 points) Suppose the population has a normal distribution, construct the exactly 95% confidence interval for the true mean µ. (c) (5 points) Suppose the population has a normal distribution, construct the 95% prediction interval for a new observation.

a) the 95% confidence interval for the true mean µ is 60.971, 65.629

The exact 95% confidence interval for the true mean µ is 60.971, 65.629

P (x`- ∝ s/√n<u <x`+ ∝ s/√n) = 0.95

Step-by-step explanation:

n= 50

x`= 63.3

s= 8.4 minutes

∝= 95%= ±1.96

The formula for calculating the confidence interval is:

x`± ∝ s/√n

Putting the values

x`± 1.96 s/√n

63.3 ± 1.96(8.4/√50)

63.3± 2.3287

60.971, 65.629

a) the 95% confidence interval for the true mean µ is 60.971, 65.629

b) Putting the values

x`± 1.96 s/√n

63.3 ± 1.96(8.4/√50)

63.3± 2.3287

The exact 95% confidence interval for the true mean µ is 60.971, 65.629

c) The prediction level tells that the drying time of the wall from 60.971 to 65.629 minutes must be in the range 95 % of the time.

And is given by

P (x`- ∝ s/√n<u <x`+ ∝ s/√n) = 0.95

you forgot the options, but i found them anyways, the correct answer is "john wilson believes that words and actions based on the intellect are superior to those based on emotions".

john wilson is depicted as an extremely intelligent man. the point of the excerpt is to make a sort of distinction between emotional and rational intelligence. he happens to have both attributes, but he clearly favors his intellectual gifts. at the same time, because of his religious background, he's a little bit conflicted with this and it makes him ashamed.

hope this !