The final exam grade of a statistics class has a skewed distribution with mean of 79 and standard deviation of 8.2. If a random sample of 35 students selected from this class, then what is the probability that average final exam grade of this sample is between 76 and 82

0.9696

Step-by-step explanation:

Given that:

Mean, m = 79

Standard deviation, s = 8.2

Sample size, n = 35

Probability that final exam grade of the sample is between 76 and 82

P(76 < x < 82)

P(x < 82) - P(x < 76)

Using the relation :

Z = (x - m) / (s/sqrt(n))

s / sqrt(n) = 8.2/sqrt(35) = 1.3860529

P(x < 82) - P(x < 76)

P[(82 - 79) / 1.3860529] - P[(76 - 79) / 1.3860529]

P(Z < 2.1644) - P(Z < - 2.1644)

Using the Z probability calculator :

0.98478 - 0.015217

= 0.969563

Hence, probability = 0.9696