I need help with the following questions (Use Ti-84)

Question

1) Of the 72 people who answered "yes" to question, 8 were male. Of the 86 people that answered "no" to the question, 10 were male. If one person is selected at random, from the group, what is the probablilty that the person answered "yes" or was male?

2) The prices that can be won in a sweepstakes are listed below togetheir with the chances of winning each other: $4900 (1 Chance in 8300); $2200 (1 Chance in 5600); $700 (1 Chance in 4300); $400, (1 chance in 2200). Find the expected value of the amount of won for one entry if the cost of entering is 65 cents.

3) The weights of certain machine components are normally distrubited with a mean of 8.3 g and a standard deviation of 0.09 g. Find the two weights that separate the top 3% and the bottom 3%. These weights could serve as limits used to identify which componets should be rejected. Round to the nearest hundreth of a gram

Answer 1

Step 1:

(1)

Out of 72 people who answered yes to the question, 8 were male.

Out of 86 people who answered no to the question, 10 were male.

Total number of people .

Number of people who answered yes to the question are 72.

Number of people who answered to the question are .

Let be the event of the person who answered yes.

Probability of the person who answered yes is .

Let be the event of the person who answered were male.

Probability of the person who answered were male is .

Probability of the person who answered yes were male is .

Find the probability of the people  who answered yes or were male is .

Probability of the people  who answered yes or were male is .

Solution:

Probability of the people  who answered yes or were male is .

Answer 2

Step 1:

(3)

The standard deviation of the weights of certain machine components σ  is 0.09 g.

Sample mean is µ = 8.3 g.

Assuming that the mean the top and bottom is 3 %.
 

Z  value for separates the top 3 % and bottom 3 %.

That value is  Z = and Z =1.88.

Let the values of the weights be x g.

x = µ + zσ

The bottom number is .

Thus, x = 8.1308 g is the weight that separates the bottom 3 %.

 

The top number is x = 8.3 + 1.88(0.09).

Thus, x = 8.4692 g is the weight that separates the top 3 %.

Solution:

The weight that separates the bottom 3 % is 8.1308 g.

The weight that separates the top 3 % is 8.4692 g.

Answer 3

Step 1:

(2)

The prices that can be won by the sweepstake are :

$4900 (1 Chance in 8300); $2200 (1 Chance in 5600); $700 (1 Chance in 4300); $400, (1 chance in 2200).

Find the Expected value.

The expected value of a discrete random variable is denoted by E, and it represents the mean value of the outcomes.

It is obtained by finding the value of , where is the probability of each outcome.

Expected value:

Expected value of the strategy is 1.3279.

As the expected value is less than 65 cents, sweepstakes is going to enter profit.

Expected value of the strategy $ 1.3279 is relevant.

Solution:

Expected value of the strategy is $ 1.3279.