Question

The value of investment properties in a certain city is normally distributed with a mean of $360,000 and standard deviation of $60,000.

(a) What is the probability that a randomly selected property is worth less than $250,000?

(b) If the value of investment properties for 5% of all investors is less than a given amount, what is the maximum amount that an investor would expect to pay for a property?

(c) If a random sample of 45 investors is selected, what is the probability that the average value of the investment property is between $106,000 and $126,000?

(d) What would be the minimum property value, on average, for 12% of the most expensive investment properties if a random sample of 50 investors were taken? Round up your final answer to two decimal places.

(e) Suppose that in the past 80% of all investors paid for their investment properties using a bank loan. However, an analyst has doubts about this figure. It is therefore decided to estimate, with 95% level of confidence, the proportion of investors who pay for their properties with a bank loan so as to be within 5% of the true proportion. How large a sample should be selected?

Answer 1