Question

The selling prices of all stocks listed on the CDNX stock exchange are known to be normally distributed with a mean of $20 and a standard deviation of $4. (a) What percentage of stocks have a selling price between $20 and $40? (b) If 167 of the stocks sell for $26 or higher, how many stocks sell on the CDNX exchange? (c) What is the minimum selling price of the most expensive 5% of stocks? (d) 2 out of every 3 stocks sells for higher than what price? (e) The prices of the middle 80% of stocks are between what two values?

Answer 1

a)

Which is where is standard normal distribution

Looking up tables we find

so that and so

Probability is

b) which comes out to be

So total number of stocks is

c) happens for is the required minimum selling price of most expensive 5% stocks

d) means so that

so that 2 out of 3 stocks sell higher than 18.28

e)

Where by symmetry

So

is what we want

So that or in other words which corresponds to (after looking up standard normal table)

So that prices of middle 80% stocks fall between

Hope this was helpful. Please do leave a positive rating if you liked this answer. Thanks and have a good day!