Question

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?

Answer 1

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.