Question

Q.1) Z is the standard normal variable. Use table 1 to determine the required probability to four decimal places. Answers should be given in the form 0.xxxx.

P(Z < -3.07)

Answer:

Q.2) X is a random variable which is normally distributed with a mean of 99.01 and a standard deviation of 15.56. Use the Excel function NORMINV to determine the required value of Xo to two decimal places. Give your answer in the form xx.xx.

P(X < Xo) = 0.0344

Answer:
Q.3) Z is the standard normal variable. Zo is a value of this variable such that

P(Z < Zo) = 0.2760

Use the Excel function NORMSINV to determine the value of Zo to two decimal places. Give your answer in the form -x.xx or x.xx as appropriate.

Answer:
Q.4) In this question, use Excel functions rather than Normal distribution tables.

The number of new cars sold by "Ma's New Car Factory" in a financial year can be approximated by a normal distribution with a mean of 125,000 cars and a standard deviation of 34,000 cars.

Part A

In order to recover all costs associated with manufacture they need to sell 100,000 cars. What is the probability that "Ma's New Car Factory" will do better than just covering their costs if the sales are distributed as expected? Give your answer to two decimal places in the form x.xx.

Answer:

Part B

What is the number of cars sales that the company has a only a 10% chance of achieving next year? Give you answer as a whole number.

Answer:

Q.5) Z is the standard normal variable. Use Table 1 to determine the required probability to four decimal places. Answers should be given in the form 0.xxxx.

P(1.02 < Z < 2.04)

Answer:

Q.6) Z is the standard normal variable. Use Table 1 to determine the required probability to four decimal places. Answers should be given in the form 0.xxxx.

P(Z > 1.78)

Answer:

Q.7) Z is the standard normal variable. Use the Excel function NORMSDIST to determine the required probability to 4 decimal places. Give your answer in the form 0.xxxx.

P(Z > 0.4545)

Answer:

Q.8) Suppose X~N(53,45.5).

In part B of this exercise you will be required to find P(X<105) using tables.

Part A

Find the value z₀ of the standard normal variable Z, such that

P(X < 105) = P(Z < z₀)

Give your answer to 2 decimal places in the form x.xx or -x.xx as appropriate.

z₀ = answer?

Part B

Use tables to find the probability P(X < 105). Give your answer rounded to 2 decimal places in the form 0.xx

Probability: answer?

Answer 1

1)

P(Z < - 3.07) = 0.0011

2)

Mean = $\mu$ = 99.01

Standard deviation = $\sigma$ = 15.56

X0 = 70.69

( Using NORMINV function)

3)

Z0 = - 0.59

( Using NORMSINV function)