Question

Question 2 Normal model

a. A cut-off score of 79 has been established for a sample of scores in which the mean is 67. If the corresponding z-score is 1.4 and the scores are normally distributed, what is the standard deviation?

b. The standard deviation of a normal distribution is 12 and 95% of the values are greater than 6. What is the value of the mean?

c. The mean of a normal distribution is 130, and only 3% of the values are greater than 155. What is the standard deviation

Answer 1

Answer: a) for probability x>a R= a-eld convert a into 7-score usi given l=67 that, a=79 , Y5 - Unknown & 7 14 ci za a-141 79 - 67 1.4 8.5714 5 - 8.5714 ) given that, and P ( 76 ) = 0.95 - P ( x-ul 6-ul ) - 0.95 -_-44 =Z^N102) - pl 2 > G-01 ) 3 0.95 12 play-1 6-4 12 = 0,05 egal)

e) P(Z > 1.64 ) = 0.05 / / from ) and (2) / -16-ell = 1.64 12 - 6+ ll (1.64 X12 ) -6 +u = 19.68 . = 19.68 +6 M = 25.68 .. mean 4 25.68 :) given that l= mean = 130 and PC x > 155 ) = 0.03 plx-ell > 155-e =0.03 => 155 - 4) = 0.03 = 0.03 P(Z > 1.88 ) from O. & 2) 55-M - 88 S 155 - 130 - 188 155-130 S. p.-r13,2978