Question

(1 point) The scores of students on the SAT college entrance μ-544.6 and standard deviation σ-25.3 (a) What is the ANSWER: that a single student randomly chosen from all those taking the test scores 548 or higher? For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test. b) What are the mean and standard deviation of the sample mean score , of 35 students? The mean of the sampling distribution for is: The standard deviation of the sampling distribution for à is: (c) What z-score corresponds to the mean score i of 548? ANSWER (d) What is the probability that the mean score of these students is 548 or higher? ANSWER: Note: You can eam partial credit on this problem. 6

Answer 1

a) P(X > 548)

= P((X - $\small \mu$ )/ $\small \sigma$ > (548 - $\small \mu$ )/ $\small \sigma$ )

= P(Z > (548 - 544.6)/25.3)

= P(Z > 0.13)

= 1 - P(Z < 0.13)

= 1 - 0.5517

= 0.4483

b) $\small \mu_{\bar x}$ = 544.6

$\small \sigma_{\bar x}$ = $\small \sigma/\sqrt n$

        = 25.3/ $\small \sqrt 35$

        = 4.2765

c) z-score = ( $\small \bar x - \mu$ )/( $\small \sigma/\sqrt n$ )

                = (548 - 544.6)/(25.3/ $\small \sqrt 35$ )

                = 0.80

d) P( $\small \bar x$ > 548)

= P(Z > 0.80)

= 1 - P(Z < 0.80)

= 1 - 0.7881

= 0.2119