Question

The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. What is the probability we could select a sample of 50 adults and find that the mean of this sample is between 98 and 103?

Answer 1

Answer: 0.7471

Step-by-step explanation:

Given : The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of $\mu=100$ and a population standard deviation of $\sigma=15$.

Sample size = 50

Using formula $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$, the z-value corresponding to x=98 will be:-

$z=\dfrac{98-100}{\dfrac{15}{\sqrt{50}}}\approx-0.94$

Z-value corresponding to x=103 will be:-

$z=\dfrac{103-100}{\dfrac{15}{\sqrt{50}}}\approx1.41$

Using the standard normal distribution table for z-scores, we have

P-value = $P(98$

Hence, the  probability we could select a sample of 50 adults and find that the mean of this sample is between 98 and 103 = 0.7471