Answer :
Answer:
the probability that the sample mean will be larger than 1224 is 0.0082
Step-by-step explanation:
Given that:
The SAT scores have an average of 1200
with a standard deviation of 60
also; a sample of 36 scores is selected
The objective is to determine the probability that the sample mean will be larger than 1224
Assuming X to be the random variable that represents the SAT score of each student.
This implies that ;
[tex]S \sim N ( 1200,60)[/tex]
the probability that the sample mean will be larger than 1224 will now be:
[tex]P(\overline X > 1224) = P(\dfrac{\overline X - \mu }{\dfrac{\sigma}{\sqrt{n}} }> \dfrac{}{}\dfrac{1224- \mu }{\dfrac{\sigma}{\sqrt{n}} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{1224- 1200 }{\dfrac{60}{\sqrt{36}} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{\dfrac{60}{6} })[/tex]
[tex]P(\overline X > 1224) = P(Z > \dfrac{24 }{10} })[/tex]
[tex]P(\overline X > 1224) = P(Z > 2.4 })[/tex]
[tex]P(\overline X > 1224) =1 - P(Z \leq 2.4 })[/tex]
From Excel Table ; Using the formula (=NORMDIST(2.4))
P(\overline X > 1224) = 1 - 0.9918
P(\overline X > 1224) = 0.0082
Hence; the probability that the sample mean will be larger than 1224 is 0.0082