It was found that 89 of medical students actually graduated

It was found that 89% of medical students actually graduated. (a) What is the probability that 10 randomly selected students would include at least 7 that graduated? (b) what is the z-score of x = 8?

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Solution

It was found that 89% of medical students actually graduated. (a) What is the probability that 10 randomly selected students would include at least 7 that graduated?

n=10

p=0.89

P( x >=7) = P( x=7)+P( x=8)+P( x=9)+P(x=10)

Binomial Probabilities Table

X

P(X)

7

0.0706

8

0.2143

9

0.3854

10

0.3118

Total

0.9822

P( x >=7)= 0.9822

(b) what is the z-score of x = 8?

Expectation = np = 8.9

Variance = np(1 - p) = 0.979

Standard deviation = 0.9894

Z score for 8, z = (8-8.9)/0.9894 = -0.9096

Z score = -0.91   ( two decimals)