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 ?

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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  

orchestra answered 1 year ago
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