Question

The SAT scores have an average of 1200 with a standard deviation of 60. A sample of 36 scores is selected.What is the probability that the sample mean will be larger than 1224? Round your answer to three decimal places.

Answer 1

Answer: 0.008

Step-by-step explanation:

Given: Mean : $\mu=1200$

Standard deviation : $\sigma = 60$

Sample size : $n=36$

The formula to calculate z-score is given by :_

$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x= 1224, we have

$z=\dfrac{1224-1200}{\dfrac{60}{\sqrt{36}}}=2.4$

The P-value = $P(z>2.4)=1-P(z$

Hence, the probability that the sample mean will be larger than 1224 =0.008