Answer:
(a) 31101
(b) $5.65
(c) $113.38
Step-by-step explanation:
The complete question is:
A regional automobile dealership sent out fliers to prospective customers indicating that they had already won one of three different prizes: an automobile valued at $20,000, a $125 gas card, or a $5 shopping card. To claim his or her prize, a prospective print on the back of the flier listed the probabilities of winning. The chance of winning the car was 1 out of 31,101, the chance of winning the gas card was 1 out of 31,101, and the chance of winning the shopping card was 31, 099 out of 31,101.
Solution:
The information provided is as follows:

(a)
The number of fliers the automobile dealership sent out is, <em>n</em> = 31,101.
This is because the probability of winning any of the three prize is out of 31,101.
(b)
Compute the expected value of the prize won by a prospective customer receiving a flier as follows:

![=[20000\times \frac{1}{31101}]+[125\times \frac{1}{31101}]+[5\times \frac{31099}{31101}]\\\\=0.6431+0.0040+4.9997\\\\=5.6468\\\\\approx 5.65](https://tex.z-dn.net/?f=%3D%5B20000%5Ctimes%20%5Cfrac%7B1%7D%7B31101%7D%5D%2B%5B125%5Ctimes%20%5Cfrac%7B1%7D%7B31101%7D%5D%2B%5B5%5Ctimes%20%5Cfrac%7B31099%7D%7B31101%7D%5D%5C%5C%5C%5C%3D0.6431%2B0.0040%2B4.9997%5C%5C%5C%5C%3D5.6468%5C%5C%5C%5C%5Capprox%205.65)
Thus, the expected value of the prize won by a prospective customer receiving a flier is $5.65.
(c)
Compute the standard deviation of the prize won by a prospective customer receiving a flier as follows:

![=\sqrt{[(20000)^{2}\times \frac{1}{31101}+(125)^{2}\times \frac{1}{31101}+(5)^{2}\times \frac{31099}{31101}]-(5.65)^{2}}\\\\=\sqrt{12854.9011}\\\\=113.37947\\\\\approx 113.38](https://tex.z-dn.net/?f=%3D%5Csqrt%7B%5B%2820000%29%5E%7B2%7D%5Ctimes%20%5Cfrac%7B1%7D%7B31101%7D%2B%28125%29%5E%7B2%7D%5Ctimes%20%5Cfrac%7B1%7D%7B31101%7D%2B%285%29%5E%7B2%7D%5Ctimes%20%5Cfrac%7B31099%7D%7B31101%7D%5D-%285.65%29%5E%7B2%7D%7D%5C%5C%5C%5C%3D%5Csqrt%7B12854.9011%7D%5C%5C%5C%5C%3D113.37947%5C%5C%5C%5C%5Capprox%20113.38)
Thus, the standard deviation of the prize won by a prospective customer receiving a flier is $113.38.