Question

The price of shares of the Continental Bank at the end of trading each day for the last year followed the normal distribution. Assume there were 240 trading days in the year. The mean price was $42.00 per share and the standard deviation was $2.25 per share. Refer to the table in Appendix B.1. (Round the final answers to 2 decimal places.)  

a-1. What percentage of the days was the price over $45.00?

Percentage of days ________ %

a-2. How many days would you estimate?

Number of days ______

b. What percentage of the days was the price between $38.00 and $40.00?

Percentage of days _______ %

c. What was the minimum price of the stock on the highest 15 days of the year?

Stocks price ________ $

Answer 1

We are given the distribution here as:

a) The probability here is computed as:

P(X > 45)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 9.12% is the required percentage here.

a-2) The number of days estimated here is computed as:
= Total number of days * Percentage of days that were price over 45

= 240*0.0912

= 21.888

Therefore 21.888 days it the estimated number of days here.

b) The probability here is computed as:

P( 38 < X < 40)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.1493 is the required probability here and therefore 14.93% is the required percentage here.

c) 15/240 = 0.0625

From standard normal tables, we have here:

P(Z > 1.534) = 0.0625

Therefore the minimum score here is computed as:
= Mean + 1.534*Std Dev

= 42 + 1.534*2.25

= 45.4515

Therefore $45.4515 is the minimum price required here.