In: Math
2. The IQ of humans is approximately normally distributed with a mean 100 and standard deviation of 15. A. What is the probablitlty that a randomly selected person has an IQ greater than 105? B. What is the probablitlty that a SPS of 60 randomly selected people will have a mean IQ greater than 105?
3. A 95% confidence interval for a population mean is (57,65). Can you reject the null hypothesis the mean= 68 at the 5% significance level why or why not?
2)
Given,
= 100 , = 15
We convert this to standard normal as
P( X < x) = P( Z < x - / )
a)
P( X > 105) = P( Z > 105 - 100 / 15)
= P (Z > 0.3333)
= 1 - P( Z < 0.3333)
= 1 - 0.6305
= 0.3695
b)
Using central limit theorem,
P( < x) = P( Z < x - / / sqrt(n) )
So,
P( > 105) = P( Z > 105 - 100 / ( 15 / sqrt(60) ) )
= ( Z > 2.5820)
= 1 - P( Z < 2.5820)
= 1 - 0.9951
= 0.0049
3)
Given, 95% confidence interval for population mean is ( 57 , 65) .
Since the claimed mean 68 is not contained in the confidence interval above, we have sufficient
evidence to reject the null hypothesis.