In: Math
A worldwide organization of academics claims that the mean IQ score of its members is 118, with a standard deviation of 16. A randomly selected group of 40 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 115.8. If the organization's claim is correct, what is the probability of having a sample mean of 115.8 or less for a random sample of this size? Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
Solution :
Given that ,
mean = = 118
standard deviation = = 16
n = 40
_{} = = 118 and
_{} = / n = 16 / 40 = 2.5298
P( 115.8) = P(( - _{} ) / _{} (115.8 - 118) / 2.5298)
= P(z -0.87)
= 0.1922 Using standard normal table,
The probability of having a sample mean of 115.8 or less for a random sample of this size is 0.192