Question

What is the expected value of a lottery ticket where there are only 1 chance in 10 millions of winning the grand prize of $50 Million, and 100,000 in 10 millions chances of winning $100?

The area under the normal curve between z = -1 and z = -2 is _______than the area under the normal curve between z = 2 and z = 3

A.equal to

B.less than

C.greater than

D.A, B, or C above depending on the value of the mean

3. as the sample size gets larger, the standard deviation of the sample mean also gets larger and larger.

True

False

4.The earnings set of data has an average of $75 with a standard deviation of $5. The probability of having more than $60 is closer to:

Answer 1

1)

expected value of a lottery ticket where there are only 1 chance in 10 millions of winning the grand prize of $50 Million

= (1/10 million) *50 million = $5

100,000 in 10 millions chances of winning $100  

= (100000/10000000) *100 = $1

Expected value = 5+1 = $6

2)

P (    -2.000   < Z <    -1.000   )                   
=    0.1587   -    0.0228   =    0.1359

P (    2.000   < Z <    3.000   )                   
= 0.9987   -    0.9772   =    0.0214

C.greater than

3)

the sample size gets larger, the standard deviation of the sample mean gets decrease

False

4)

.The earnings set of data has an average of $75 with a standard deviation of $5. The probability of having more than $60 is closer to:

µ =    75              
σ =    5              
                  
P ( X ≥   60.00   ) = P( (X-µ)/σ ≥ (60-75) / 5)          
= P(Z ≥   -3.000   ) = P( Z <   3.000   ) =    0.9987

Please revert back in case of any doubt.

Please upvote. Thanks in advance.