Question

The average GRE score at the University of Pennsylvania for the incoming class of 2016-2017 was 311 with a standard deviation of 13.5. If you select a random sample of 60 students, what is the probability that the sample mean will be less than 314? Round your answer to three decimal places.

Answer 1

Answer 2

1. Given:

• Population mean (μ) = 311

• Population standard deviation (σ) = 13.5

• Sample size (n) = 60

• Sample mean we're evaluating (x̄) = 314

• 
  

2. Calculate the standard error (SE) of the sample mean:

   $$SE=\frac{\sigma }{\sqrt{n}}=\frac{13.5}{\sqrt{60}}\approx 1.742$$

4. Compute the z-score for the sample mean of 314:

   $$z=\frac{\bar{x}-\mu }{SE}=\frac{314-311}{1.742}\approx 1.722$$

6. Find the probability corresponding to this z-score:
   Using a standard normal distribution table or calculator, the probability that $z<1.722$ is approximately 0.957.

7. 
   

8. Answer is :-
   The probability that the sample mean will be less than 314 is approximately 0.957, or 95.7% when rounded to three decimal places.