Question
In: Statistics and Probability
Based upon extensive data from a national high school educational testing program, the mean score of...
Based upon extensive data from a national high school educational testing program, the mean score of national test scores for mathematics was found to be 605 and the standard deviation of national test scores for mathematics was found to be 98 points. What is the probability that a random sample of 196 students will have a mean score of more than 610? Less than 591?
a) The probability that a random sample of 196 students will have a mean score of more than 610 is ?
b) The probability that a random sample of 196 students will have a mean score of less than 591 is ?
Solutions
Expert Solution
Solution :
Given that ,
mean = 
= 605
standard deviation = 
= 98
n = 196
=
= 605
=
/ 
n = 98 /
196 = 7
a) P( > 610) = 1 - P( < 610)
= 1 - P((
-
) /
< (610 - 605) / 7 )
= 1 - P(z < 0.71)
Using z table
= 1 - 0.7611
= 0.2389
b) P( < 591) = P((
-
) /
< (591 - 605) / 7)
= P(z < -2.00)
Using z table
= 0.0228
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