Question

5)

A manufacturer of paper used for packaging requires a minimum strength of 1600 g/cm². To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour's production and a strength measurement is recorded for each. The standard deviation σ of the strength measurements, computed by pooling the sum of squares of deviations of many samples, is known to equal 160 g/cm², and the strength measurements are normally distributed.

(a) What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?

-The sampling distribution is nonnormal with mean μ and standard deviation 160.

-The sampling distribution is nonnormal with mean μ and standard deviation 160/$\sqrt{10}$
-The sampling distribution is normally distributed with mean μ and standard deviation 160/$\sqrt{10}$

-The sampling distribution is normally distributed with mean 10 and standard deviation 160.

-The sampling distribution is normally distributed with mean μ and standard deviation 160.

(b) If the mean of the population of strength measurements is 1650 g/cm², what is the approximate probability that, for a random sample of n = 10 test pieces of paper, x < 1600? (Round your answer to four decimal places.)


(c) What value would you select for the mean paper strength μ in order that

P(x̄ < 1600) be equal to 0.001? (Round your answer to three decimal places.)

= g/cm²

6)

Allen Shoemaker derived a distribution of human body temperatures with a distinct mound shape. Suppose we assume that the temperatures of healthy humans are approximately normal with a mean of 37° Celsius and a standard deviation of 0.2 degrees.

(a) If 135 healthy people are selected at random, what is the probability that the average temperature for these people is 36.74°C or lower? (Round your answer to four decimal places.)

(b) Would you consider an average temperature of 36.74°C to be an unlikely occurrence, given that the true average temperature of healthy people is 37°C? Explain.

-Since the probability is near 0.5, the average temperature of 36.74°C is likely.

-Since the probability is extremely large, the average temperature of 36.74°C is very likely.

-Since the probability is extremely small, the average temperature of 36.74°C is very unlikely.

-Since n is small, the average temperature of 36.74°C is unlikely.

-Since n is large, the average temperature of 36.74°C is likely.

Answer 1

Sals Ps X~(M, ) Standard deviation 6 160 a) it is given strength meakserment (sayx) harmally distribeiled i.e, X ~N (4,160) According to central limit thearem, of X~ N(M, 6) then sample mean is also narmally distributed i.e., e han 160 To the sampling distribution is normally dister buted with mean is and standard duration 160NTO population mean = 1650 = U P(x21600) Plx-Mc 1600-M P(x-4 Transfagun x inlo Standard narmal vacuche Z = X-4 X-4; P(xe1600) - P(Z< -0.3125) P(x1600)=P(ZC-0.3125) = 0.37828 P(x<1600)=P(x-M2 1600-4 (By using z table) = 0.001 P(Z < 1600-4 300-4) = 0.001 (By using a scare) get x-scare for which the probabt- lédy is rongly equal to o.olpe, x-scare =-2:32 1600-4 -2.32 = 1600-M =-2.32 M=1717.4 we that 160/10