Question

1. Let  z be a normal random variable with mean 0 and standard deviation 1. What is P(-2.25 <  z < -1.1)?

		0.1235
		0.3643
		0.8643
		0.4878

You are offered an investment opportunity. Its outcomes and probabilities are presented in the following table.

x	P(x)
-$1,000	.40
$0	.20
+$1,000	.40 ​

2. The mean of this distribution is _____________.

		$400
		$0
		$-400
		$200

3. T/F. The probability that the complement of an event will occur is given by P(E') = 1 - P(E)

True

False

4.

A recent survey of local cell phone retailers showed that of all cell phones sold five years ago, 64% had a camera, 28% had a music player, and 22% had both. The probability that a cell phone sold five years ago did not have either a camera or a music player is

		.92
		.18
		.70
		.30

5.

The sample standard deviation is related to the sample variance through what functional form?

		Square root
		Linear
		Exponential
		Logarithm

6.

A large industrial firm allows a discount on any invoice that is paid within 30 days. Of all invoices, 10% receive the discount. In a company audit, 10 invoices are sampled at random. The binomial probability that fewer than 3 of the 10 sampled invoices receive the discount is approximately_______________.

		0.9298
		0.0571
		0.3486
		0.1937

7.

Suppose x is a normal random variable with mean 60 and standard deviation 2. A z score was calculated for a number, and the z score is 3.4. What is the inverse normal calculation of x?

		56.6
		66.8
		68.6
		63.4

Answer 1

1. Let  z be a normal random variable with mean 0 and standard deviation 1. What is P(-2.25 <  z < -1.1)?

Using Normal Table

P(-2.25 <  z < -1.1) = P(z < -1.1) - P(z < -2.25) = 0.1357 - 0.0122 = 0.1235

• o.1235

You are offered an investment opportunity. Its outcomes and probabilities are presented in the following table.

2. The mean of this distribution is _____________.

• $0

3. T/F. The probability that the complement of an event will occur is given by P(E') = 1 - P(E)

True

4.

A recent survey of local cell phone retailers showed that of all cell phones sold five years ago, 64% had a camera, 28% had a music player, and 22% had both. The probability that a cell phone sold five years ago did not have either a camera or a music player is

P (not have either a camera or a music ) = 1 - P( either a camera or a music )

= 1- [P(camera)+P(music)-P(both)]

= 1 - [0.64+0.28-0.22] = 0.30

• 0.30

5.

The sample standard deviation is related to the sample variance through what functional form?

• Square root

6.

A large industrial firm allows a discount on any invoice that is paid within 30 days. Of all invoices, 10% receive the discount. In a company audit, 10 invoices are sampled at random. The binomial probability that fewer than 3 of the 10 sampled invoices receive the discount is approximately_______________.

p = 0.10 , n = 10

Using Binomial distribution in excel

P( x < 3 ) =BINOMDIST(2,10,0.1,1) = 0.9298

• 0.9298

​​​​​​​

7.

Suppose x is a normal random variable with mean 60 and standard deviation 2. A z score was calculated for a number, and the z score is 3.4. What is the inverse normal calculation of x?

x = 3.4*2+60 = 66.8

• 66.8