Please Help! A statistician\'s teenage daughter withdraws a certain amount of mo
ID: 3132078 • Letter: P
Question
Please Help!
A statistician's teenage daughter withdraws a certain amount of money X from an ATM every so often, using a method that is unknown to him: she randomly spins a circular wheel that is equally divided among four regions, each containing a specific dollar amount, as shown. Bank statements reveal that over the past n = 80 ATM transactions, $10 was withdrawn thirteen times, $20 sixteen times, $30 nineteen times, and $40 thirty-two times. For this sample, construct a relative frequency table, and calculate the average amount 3c withdrawn per transaction, and the variance s^2. Suppose this process continues indefinitely. Construct a probability table, and calculate the expected amount p withdrawn per transaction, and the variance sigma^2. (Verify that, for this sample, s^2 and sigma^2 happen to be equal.)Explanation / Answer
x
f
Relative frequency p
10
13
0.1625
20
16
0.2
30
19
0.2375
40
32
0.4
80
X
P(X)
x*p(x)
(x-mean)^2*p(x)
10
0.1625
1.625
57.12891
20
0.2
4
15.3125
30
0.2375
7.125
0.371094
40
0.4
16
50.625
Total
1.000
28.75
123.4375
Mean =28.75
Variance=123.4375
For the population,
X
P(X)
x*p(x)
(x-mean)^2*p(x)
10
0.25
2.5
56.25
20
0.25
5
6.25
30
0.25
7.5
6.25
40
0.25
10
56.25
Total
1.000
25
125
Mean =25
Variance=125
Population variance is larger than the sample variance.
x
f
Relative frequency p
10
13
0.1625
20
16
0.2
30
19
0.2375
40
32
0.4
80