Question

Assume the average stock price for companies making up the S&P 500 at certain time period is $40, and the standard deviation is $10. Assume the stock prices are normally distributed. How high does a stock price have to be to put a company in the bottom 5%?

		$27.20
		$20.40
		$23.55
		$18.78

Answer 1

Given that the average stock price for companies making up the S&P 500 at certain time period is $40

So = 40

the standard deviation is $10

So = 10

To be in the bottom 5%, there should be 5% of the companies that have a lower stock price than that stock price

So the area to the left of z-score should be 0.05

The z-score that has an area of 0.05 to its left = -1.6449 from the online calculator

z-score = (X - ) /

-1.6449 = (X - 40) / 10

X - 40 = 10 * (-1.6449)

X - 40 = -16.449

X = 40 - 16.449

X = 23.551

X = 23.55 rounded to 2 decimal places

So Answer is Option C