Respuesta :
Answer:
Probability of having a sample mean of 114.6 or less is 0.8315.
Step-by-step explanation:
We are given that worldwide organization of academics claims that the mean IQ score of its members is 112, with a standard deviation of 16.
A randomly selected group of 35 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 114.6.
Let [tex]\bar X[/tex] = sample mean
The z score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean IQ score of its members = 112
[tex]\sigma[/tex] = standard deviation = 16
n = sample of members = 35
Now, probability of having a sample mean of 114.6 or less is given by = P([tex]\bar X[/tex] [tex]\leq[/tex] 114.6)
P([tex]\bar X[/tex] [tex]\leq[/tex] 114.6) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{114.6-112}{\frac{16}{\sqrt{35} } }[/tex] ) = P(Z [tex]\leq[/tex] 0.96)
= 0.8315
Hence, the required probability is 0.8315.
