A survey of American Society of Investors found 30 of indivi

A survey of American Society of Investors found 30% of individual investors have used a discount broker.

In a random sample of nine individuals, what is the probability:

a.    Exactly two of the sample individuals have used a discount broker? P(x = 2)

Enter answers to 4 decimal places with 0 to the left of the decimal point.

b.    None of the 9 individuals have used a discount broker. P(X = 0)

Enter answers to 4 decimal places with 0 to the left of the decimal point.

c.    Two or three individuals have used a discount broker. P( 2 <= X <= 3)

Enter answers to 4 decimal places with 0 to the left of the decimal point.

d.    What is the mean and standard deviation for this distribution?

Enter each answer to 2 decimal places.

Solution

A survey of American Society of Investors found 30% of individual investors have used a discount broker.

In a random sample of nine individuals, what is the probability:

n=9

P=0.3

a.    Exactly two of the sample individuals have used a discount broker? P(x = 2)

Enter answers to 4 decimal places with 0 to the left of the decimal point.

P( x=2) =0.2668

b.    None of the 9 individuals have used a discount broker. P(X = 0)

Enter answers to 4 decimal places with 0 to the left of the decimal point.

P( x=0) =0.0404

c.    Two or three individuals have used a discount broker. P( 2 <= X <= 3)

Enter answers to 4 decimal places with 0 to the left of the decimal point.

P( 2 <= X <= 3) = P( x=2)+P( x=3)

=0.2668+0.2668

=0.5336

d.    What is the mean and standard deviation for this distribution?

Enter each answer to 2 decimal places.

mean = np = 2.7

Variance = np(1 - p) = 1.89

Standard deviation = 1.37