The probability that the mean of their test scores is greater than 78 is 0.0301.
Given,
Mean = 73
Standard Deviation σ = 7.8
Number of students randomly selected = 24
Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
For an experiment having 'n' number of outcomes, the number of favorable outcomes can be denoted by x.
The formula to calculate the probability of an event is as follows.
Probability(Event) = Favorable Outcomes/Total Outcomes = x/n
The number of standard deviations from the mean is called the z - score and can be found by the formula
Z = (x - μ)/σ.
Z = (70 - 73)/(7.8/√24) = -1.88442228
P(z < -1.88) = 0.0301
Therefore, P(z < -1.88) = 0.0301
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