Question #1
Section 6.1 mean of a discrete random variable: page 302
Find the sum of the products of the random variable and the probability of observing that value (x) of the random variable.
Here is what you want to do:
If you were doing it “by hand” with no calculator:
Mean = 0(0.296) + 1(0.176) + 2(0.343) + 3(0.079) + 4(0.106)
= 1.523 round to one decimal place and you get 1.5
Standard deviation (page 304)
If you were doing it “by hand” with no calculator:
Take the square root of [(0 – 1.5)2 * (0.296) + (1- 1.5) 2 * (0.176) + (2- 1.5) 2 * (0.343) + (3- 1.5) 2 * (0.079) + (4- 1.5) 2 * (0.106)] =
square root ()
= 1.189 …
round to one place and you get 1.2
Here is how to do it WITH the calculator:
Put the x values in L1 and P(x) values in L2
Have the calculator give you “1-Var Stats” for L1, L2. (The “comma” is above the number 7.)
Find 1-Var Stats for L1, L2
Scroll down to lower screen to see standard deviation
“x-bar” is the mean, 1.5 (rounded to nearest tenth) and sigma x is the standard deviation, 1.27885 … (so rounded to the nearest
tenth is 1.3).
Therefore the standard deviation is 1.3.
This is the definition of P(3) which is given in the table as 0.079.
If it asked “three or more” you would add P(3) + P(4) = 0.079 + 0.106 = 0.185
Or if it asked “2 or fewer activies” you would add P(2) + P(1) + P(0) = 0.343 + 0.176 + 0.296 = 0.815
And so on . . .
Question #2
Section 6.1 mean of a discrete random variable: page 302
Find the sum of the products of the random variable and the probability of observing that value (x) of the random variable.
Mean = 0(0.0526) + 1(0.4987) + 2(0.2041) + 3(0.1028) + 4(0.1262) + 5(0.0156)
= 1.7981 round to one decimal place and you get 1.8
Standard deviation (page 304)
Take the square root of [(0 – 1.7981)2 * (0.0526) + (1- 1.7981) 2 * (0.4987) + (2- 1.7981) 2 * (0.2041) + (3- 1.7981) 2 * (0.1028) + (41.7981) 2 * (0.1262) + (5- 1.7981) 2 * (0.0156) ] = square root (1.416)
= 1.189 …
round to one place and you get 1.2
Enter x values into L1 and P(x) values into L2
Find 1-Var Stats for L1, L2
Scroll down to lower screen to see standard deviation
“x-bar” is the mean, 1.8 and sigma x is the standard deviation, 1.2.
Question #3
This fits the definition of a discrete random variable (see section 6.1). To find the expected value, we need to find the mean. So we
will need to multiply the probabilities of each random variable times the random variable.
The company will make $210 if the person survives and the probability of that is 0.999556. If she dies, they will lose (190,000 –
210) = 189, 790. Since they will lose it, this is a negative amount for them. The probability that she dies is the complement of the
probability that she lives, so 1 – 0.999556 which is 0.000444.
x
$210 (survives)
-$189,790 (dies)
P(x)
0.999556
0.000444
x*P(x)
$209.91
-$84.27
The sum of x * P(x) = $209.91 + (- $84.27)
= $125.64