Show work 1:17 PM webworklans.camosun.ca 00 Bell , 3196. (1 pt) The scores of st

Question

Show work 1:17 PM webworklans.camosun.ca 00 Bell , 3196. (1 pt) The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean 553.2 and standard deviation 29.4. (a) What is the probability that a single student randomly chosen from all those taking the test scores 560 or higher? ANSWER: For parts (b) through (d), consider a simple random sample (SRS) of 30 students who took the test. (b) What are the mean and standard deviation of the sample mean score C, of 30 students? The mean of the sampling distribution for is:

Explanation / Answer

a)

z-score corresponding to 560 = (560-553.2)/29.4 = 0.2312

P( scores 560 or higher ) = P ( z > 0.2312 ) = 1 - P ( z < 0.2312) = 1 -0.5914 = 0.4085

b)

mean( x_bar ) = 553.2

standard devaition (x_bar) = 29.4/sqrt(30) = 5.3676

c)

z-score corresponding to x_bar of 560 = (560-553.2)/5.3676 = 1.2668

d)

P( x_bar > 560 ) = P (z > 1.2668 ) = 1 - P( z< 1.2668 ) = 1 - 0.8973 = 0.1026

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