Question

The final exam grade of a statistics class has a skewed distribution with a mean of 78 and a standard deviation of 7.8. If a random sample of 36 students selected from this class, then what is the probability that the average final exam grade of this sample is between 75 and 80? (round to 4 decimal places)

Answer 1

This is a normal distribution question with

Sample size (n) = 36
Since we know that

P(75.0 < x < 80.0)=?

This implies that
P(75.0 < x < 80.0) = P(-2.3077 < z < 1.5385) = P(Z < 1.5385) - P(Z < -2.3077)
P(75.0 < x < 80.0) = 0.9380 - 0.0105
P(75.0 < x < 80.0) = 0.9275
PS: you have to refer z score table to find the final probabilities.
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