a. What is the probability of randomly selecting a score less than X = 51? h. Wh

Question

a. What is the probability of randomly selecting a score less than X = 51? h. What is the probability of selecting a sample of n#: 4 scores with a mean less than M 51? c. What is the probability of selecting a sample of n=36 scores with a mean less than M 51? 16. A population of scores fomms a normal distribution with amean of =80and a standard deviation of 10. a. What proportion of the scores have values between 75 and 852 h. For samples on 4yhat proportion of the samples will have means between 75 and 852

Explanation / Answer

Solution:

Given information
= 80, = 10
a) The proportion of the scores have values between 75 and 85
P ( 75 < X < 85 ) = P ( 7580/10 < X/ < 8580/10)
= P ( 0.5 < Z < 0.5 )
= P ( Z < 0.5 )P (Z < 0.5 )
= 0.6915 - 0.3085
= 0.383
b) Sample size n = 4
The proportion of the samples will have means between 75 and 85
P ( 75 < X < 85 ) = P ( 7580/(10/4) < X/(/n) < 8580/(10/4))
= P ( 7580/5 < Z < 8580/5 )
= P ( Z < 1.00 )P (Z < 1.00 )
= 0.8413 - 0.1587
= 0.6827

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