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In: Statistics and Probability

Let X be the exam grade of a student taking Calculus 1 with Professor Smith. The...

Let X be the exam grade of a student taking Calculus 1 with Professor Smith. The professor believes that X has a mean of 76 and a standard deviation of 12.5. Suppose there are 100 students in Professor Smith's class. Approximate the probability that X is between 73.8 and 77.8.

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Expert Solution

Solution :

Given that,

mean = = 76

standard deviation = = 12.5

n = 100

= = 76

= / n = 12.5 / 100 = 1.25

P(73.8 < < 77.8)  

= P[(73.8 - 76) /1.25 < ( - ) / < (77.8 - 76) / 1.25)]

= P(-1.76 < Z < 1.44)

= P(Z < 1.44) - P(Z < -1.76)

Using z table,  

= 0.9251 - 0.0392   

= 0.8859

orchestra answered 2 years ago
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