A global study in 2010 shows IQ scores is normally distributed with the mean of 89.8 and standard deviation of 10.7.

(a) If the Indonesian population is 250 million people, how many Indonesians have IQ between 79.1 and 100.5?

(b) A random sample of 16 people from all across the globe gives the mean IQ of 80. Is it true that the probability that the sample mean is 80 or less is less than 1%? Explain.

(c) Use information from question 3(b) above to find the most precise estimate of the confidence interval of the mean using 95% level of confidence.

(d) A national survey in Indonesia was conducted with a sample size of 22,500 people and reveals a sample mean of 78. Can we reject the null hypothesis of 89.8 at 0.1% significance level? Explain