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Use the central limit theorem to solve the problem. Quiz scores for Grammer 222 class are...

Use the central limit theorem to solve the problem.

Quiz scores for Grammer 222 class are normally distributed with a mean of 60.5 and a standard deviation of 10.5.

1. If a student is chosen, find the probability that this student's score is at least 70.2?

2. If a sample of 22 students is randomly selected, find the probability that their mean score is at least 70.2?

Solutions

Expert Solution

Solution :

Given that ,

1) P(x 70.2) = 1 - P(x   70.2)

= 1 - P[(x - ) / (70.2 - 60.5) / 10.5]

= 1 -  P(z 0.92)

= 1 - 0.8212

= 0.1788

2) = 60.5

= / n = 10.5 / 22 = 2.24

P( 70.2) = 1 - P( 70.2)

= 1 - P[( - ) / (70.2 - 60.5) / 2.24]

= 1 - P(z 4.33)   

= 1 - 1

= 0

orchestra answered 2 years ago
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