5 (5.1-5.4) (Type integers or decimals.) O A. The shape is that of a uniform dis

Question

5 (5.1-5.4) (Type integers or decimals.) O A. The shape is that of a uniform distribution and depends on the O B. The shape is that of a unidorm distribution and does not depend on the sample size. O c. The shape is that of a normal distribution and depends on the sample size. O D. The shape is that of a normal distrbution and does not depend on the sample size. c. Calculate the standard normal z-score corresponding to a value of x-22.7 (Type an integer or a decimal.) d. Calculate the standard normal z-score corresponding to a value of x 26.6. Type an integer or a decimal.) e. Find P (x

Explanation / Answer

Solution:- Given that mean = 23 , sd = 21 , n = 49
a. x = 23
x = 21/sqrt(49) = 3

b. option c. The shape is that of a normal distribution and depends on the sample size

c. Z = (x - )/(/sqrt(n)) = (22.7-23)/3 = -0.1

d. Z = (26.6-23)/3 = 1.2

e. P(X < 22.7) = P(Z < -0.1) = 1P(Z < 0.1) = 1 0.5398 = 0.4602

f. P(X > 26.6) = P(Z > 1.2) = 1P(Z < 1.2) = 1 0.8849 = 0.1151

g. P(22.7 < X < 26.6) = P( -0.1 < Z < 1.2) = 0.4247

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