Math 109!
Practice Exam 2
1. Name: Key
2. Decide whether the random number is discrete or continuous:
a. The weight of babies between 6 and 9 months old: CONTINUOUS
b. The amount of gas used by SUVʼs driven in the United States: CONTINUOUS
3. Determine whether the following distribution is a
probability distribution:
x
In order to be a Probability distribution the
following must be true:
0 ≤ P(x) ≤ 1
and
∑P(x) ≅ 1,
so
∑P(x) = 0.353 + 0.45 + 0.037 = 0.84
p(x)
1
0.353
2
0.45
3
0.037
Thus it is not a Probability Distribution!
4. Use the frequency distribution table to construct a probability distribution.
Hits
Games
Hits
P(x)
x*P(x)
(x - μ)2P(x)
0
29
0
0.20714286
0
0.346235058
1
62
1
0.44285714
0.4429
0.037981778
2
33
2
0.23571429
0.4714
0.117869169
3
12
3
0.08571429
0.2571
0.249800292
4
3
4
0.02142857
0.0857
0.15704191
5
1
5
0.00714286
0.0357
0.09816363
Σ=
1.2929
1.007091837
Σ=
140
5. Use the probability table above to calculate the:
a. mean:μ = 1.3
b. variance: σ2 = 1.0
c. standard deviation: σ = 1.0
d. Expected value: E(x) = μ = 1.3
!
1 of 4
Math 109!
Practice Exam 2
6. One in four adults in the united states owns individual stocks. In a random sample of
12 people, what is the probability that the number owning individual stocks is:
n = 12, p = 1/4 = 0.25, q = 1 - p = 0.75, x = 0, 1, 2, 3, ..., 12
a. exactly two: p(x) = 12C2p2q10 = 0.2322
b. at least two: P(x ≥ 2) = 1 - P(x < 2) = 1 - (P(0) + P(1)) = 1 - 0.032 - 0.13 = 0.841
c. more than two:
P(x > 2) = 1 - P(x ≤ 2) = 1 - (P(0) + P(1) + P(2)) = 1 - 0.032 - 0.13 - 0.232 = 0.61
7. Determine/identify which graph has the greater standard deviation and which has
the smallest standard deviation:
!
2 of 4
Math 109!
Practice Exam 2
8. Find the area of the indicated region under the standard normal curve: z = 1.5
Looking up on the table provides p(z < 1.5) = 0.9332
9. Find the probability indicated by the curve on the standard normal curve below: We
need to solve: P( -0.5 < z < 2) = P(z < 2) - P(z < -0.5) = 0.9772 - 0.3085 = 0.6687
!
3 of 4
Math 109!
Practice Exam 2
10. The weights of adult male beagles are normally distributed, with a mean of 25
pounds and a standard deviation of 3 pounds. A beagle is randomly selected.
a. Find the probability that the beagle weights less than 23 pounds:
p( x < 23 ) = p(z < -0.67) = 0.2514
b. Find the probability that the beagleʼs weight is between 23 and 25 pounds:
p(23 < x < 25) = p(z < 0) - p(z < -0.67) = 0.50 - 0.2514 = 0.2486
c. Find the probability that the beagle weights more than 27 pounds:
p(x > 27) = p(z > 0.67) = 1 - p(z < 0.67) = 1 - 0.7486 = 0.2514
!
4 of 4