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(For questions 1 and 2) A burger restaurant offers a promotion. With the purchase of every meal, you get a coupon to use for your next purchase. 85\(\%\) of the coupons are worth $1, 10\(\%\) of the coupons are worth $2, 4\(\%\) of the coupons are worth $5. And 1\(\%\) of the coupons are worth $20.

1.  Find the expected value, \(\mu\), of the coupon.

a.  $1.45

b.  $1.85

c.  $2.25

d.  $2.65

d.  $3.05

2.  Find the standard deviation, \(\sigma\), for the value of the coupon.

a.  $1.80

b.  $2.04

c.  $3.33

d.  $4.23

d.  $5.94

3.  If you flip a fair coin 10 times, find the probability of flipping exactly 5 heads (rounded to the nearest 1%.

a.  15%

b.  25%

c.  35%

d.  45%

d.  55%

4.  Assuming that birthdays are uniformly distributed among 365 days in a year, compute the probability that in a randomly selected group of 40 people, at least two share a birthday.

a.  11.0\(\%\)

b.  29.3\(\%\)

c.  60.1\(\%\)

d.  78.8(\%\)

d.  89.1\(\%\)

(For questions 5 to 9) The chance of winning a particular game is \(\frac{1}{4}\). Say we play the game 10 times.

5.  Find the chance of winning exactly two times.

a.  23.5\(\%\)

b.  25.6\(\%\)

c.  28.2\(\%\)

d.  29.8\(\%\)

d.  30.1\(\%\)

6.  Find the chance of winning fewer than 3 times.

a.  52.6\(\%\)

b.  60.6\(\%\)

c.  70.4\(\%\)

d.  75.2\(\%\)

d.  77.6\(\%\)

7.  Find the chance of winning at least 3 times.

a.  22.4\(\%\)

b.  24.8\(\%\)

c.  29.6\(\%\)

d.  39.4\(\%\)

d.  47.4\(\%\)

8.  If r denotes the the number of wins, find the expected value, \(\mu\) for r.

a.  1

b.  1.5

c.  2

d.  2.5

d.  3

9.  If r denotes the the number of wins, find the standard deviation,\(\sigma\) for r.

a.  1.20

b.  1.32

c.  1.37

d.  1.88

d.  1.95