the final exam grade of a statistics class has a skewed distribution with mean of 76 and standard deviation of 7.6. if a random sample of 32 students selected from this class, then what is the probability that average final exam grade of this sample is between 75 and 80?

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

What is standard deviation?

Standard Deviation is a measure which shows how much variation (such as spread, dispersion, spread,) from the mean exists. The standard deviation indicates a “typical” deviation from the mean.

Given,

mean = 76

total number n = 36

standard deviation =7.6

Probability that the exam grade lies between 75 and 80.

P(75 < x < 80)

P(x < 80) - P(x < 75)

Using the relation :

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

Z = 7.6/[tex]\sqrt{36}[/tex] = 1.3435

Now,

P(x < 80) - P(x < 75)

P[(80-76) / 1.3435] - P[(75-76) / 1.3435]

= 0.7702

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