A. Let K be a variable with mean 152 and standard deviation of 12. Let Z be the

Question

A. Let K be a variable with mean 152 and standard deviation of 12. Let Z be the standardized version of K . Find a number a such that the event K = 141.8 is equivalent to Z =a .

B. Let K be a variable with mean 152 and standard deviation of 12. Let Z be the standardized version of K . Find a number b such that the event Z = 0.35 is equivalent to K = b .

C. Let K be a variable with mean 152 and standard deviation of 12. Let Z be the standardized version of K . Find numbers c and d such that the event 139.4 < K 158.6 is equivalent to c < Z d . (Enter as a pair (c ,d ).)

D. Let K be a variable with mean 152 and standard deviation of 12. Let Z be the standardized version of K . Find numbers p and q such that the event 2.25 < Z < 2.65 is equivalent to p < K < q . (Enter as a pair (p ,q ).)

E. Consider a normally distributed variable R with mean of 244 and a standard deviation of 20. Find P (R < 236).

F. Consider a normally distributed variable R with mean of 244 and a standard deviation of 20. Find P (236 < R < 257).

G. Consider a normally distributed variable R with mean of 244 and a standard deviation of 20. Find b such that P (R < b ) = 0.1357 .

H. The defect rate for a production line is 14%. Suppose 270 units are to be produced. (You may assume that the relative frequency of defects out of 270 is roughly normal.) Give a 95% Confidence Interval for the relative frequency of defectives in the batch of 270.

I. The defect rate for a production line is 14%. Suppose 270 units are to be produced. Give a 95% Confidence Interval for the actual number of defectives.

Explanation / Answer

A. Mean = 152 and standard deviation = 12

So, Z = (K - mean)/ std. dev. = (141.8 - 152)/12 = - 0.85

B. HEre Z = 0.35

Z = (K - mean)/ std. dev. = 0.35 = (K - 152)/12

K = 152 + 0.35 * 12 =156.2

C. Z1 = c = (139.4 - 152)/12 = -1.05

Z2 = d = (158.6 - 152)/12 = 0.55

(c,d) = (-1.05, 0.55)

d. p = MEan + Z * std. dev. = 152 + 2.25 * 12 = 179

q =MEan + Z * std. dev.= 152 + 2.65* 12 = 183.8

(p,q) = (179, 183.8)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.