SOLUTION: A final exam in Statistics has a mean of 73 with a standard deviation of 7.73. Assume that a random sample of 24 students is selected and the mean test score of the sample is comp

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Question 1077402: A final exam in Statistics has a mean of 73 with a standard deviation of 7.73. Assume that a random sample of 24 students is selected and the mean test score of the sample is computed. What percentage of sample means are less than 70?
mean of sample 7.73/sq root 24 7.73/4.9 = 1.6
z(70)= (70-73)/1.6 = -3/1.6 = -1.85
P (x<70) = P(z<-1.85) = ???
Help?
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Standard Error = SE
SE = s/sqrt(n)
SE = 7.73/sqrt(24)
SE = 1.57787964264283

Standard Z score
z = (x - mu)/SE
z = (70-73)/1.57787964264283
z = -1.9012856994436
z = -1.90

Now use a table to find the area to the left of z = -1.90
With that table, look at the row that has -1.9 and the column with 0.00. The intersection of this row and column combo has 0.0287 in the cell

This means that
P(Z < -1.90) = 0.0287
P(xbar < 70) = 0.0287
This is approximate of course. To get better accuracy, a calculator is recommended.

Since the area is 0.0287, the percentage of sample means less than 70 is roughly 2.87% which is the final answer.