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

Explanation:

Given: Mean :
`\mu=1200`

Standard deviation :
`\sigma = 60`

Sample size :
`n=36`

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

`z=(x-\mu)/((\sigma)/(√(n)))`

For x= 1224, we have

`z=(1224-1200)/((60)/(√(36)))=2.4`

The P-value =
`P(z>2.4)=1-P(z<2.4)=1-0.9918024=0.0081976\approx0.008`

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