Question 207750: Section 4.1 Probability Distribution
1. Decide whether the random variable is discrete or continuous.
(References: example 1 page 195, end of section exercises 13 – 20 page 201) (1 points per each part)
a. The cost of a randomly selected apple
b. The height of randomly selected Statistics student
c. The number of books in the local college library
d. The braking time of a motorcycle
e. The number of cell phone call between Bagdad and Ft Bragg, NC on Christmas day in the current year
2. Decide whether the distribution is a probability distribution. If it is not as probability distribution, identify the property that is not satisfied. (References: example 3 and 4 page 197, end of section exercises 25 - 28 page 202 - 203)
x P(x)
0 0.49
1 0.05
2 0.32
3 0.07
4 0.07
3. A batch of 4 computers and the probabilities associated with the defectives in the group. Complete the table shown and find the mean, variance, and standard deviation for the distribution. Round a – c to 2 decimal places.
(References: example 5 and 6 page 198 - 199, end of section exercises 29 - 34 page 203)
x P(x) x P(x) x - (x - )2 P(x) (x - )2
0 0.34
1 0.17
2 0.26
3 0.21
4 0.02
x P(x) = P(x) (x - )2 =
(5 points for table)
a. Mean
(2 points)
= 1.596
b. Variance 2
(2 points)
=1.204784
Section 4.2: Binomial Probability
Find the indicated binomial probabilities. Round to the nearest 3 decimal places. (References: example 6 page 212, end of section exercises 15 - 24 page 216 - 217) For part d and e: (References: example 8 page 214)
4. The probability that a pumpkin seed will germinate is 70%. A gardener plants in batches of 12. (1 points each)
a. What is the probability that exactly 10 seeds will germinate?
b. What is the probability that 10 or more will germinate?
c. What is the probability that all seeds will germinate?
d. Find the mean
e. Find the variance 2
5. A True-False test has 20 questions with each having 2 possible answers with one correct. Assume a student answers every question.
a. What is the probability of getting exactly 9 correct answers?
b. What is the probability of getting less than 6 correct answers?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Section 4.1 Probability Distribution
1. Decide whether the random variable is discrete or continuous.
(References: example 1 page 195, end of section exercises 13 – 20 page 201) (1 points per each part)
a. The cost of a randomly selected apple: discrete
-----------------------
b. The height of randomly selected Statistics student: continuous
-----------------------
c. The number of books in the local college library: discrete
-----------------------
d. The braking time of a motorcycle: discrete
-----------------------
e. The number of cell phone call between Bagdad and Ft Bragg, NC on Christmas day in the current year: discrete
-----------------------
2. Decide whether the distribution is a probability distribution. If it is not a probability distribution, identify the property that is not satisfied. (References: example 3 and 4 page 197, end of section exercises 25 - 28 page 202 - 203)
x P(x)
0 0.49
1 0.05
2 0.32
3 0.07
4 0.07
---
It is a probability distribution
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3. A batch of 4 computers and the probabilities associated with the defectives in the group. Complete the table shown and find the mean, variance, and standard deviation for the distribution. Round a – c to 2 decimal places.
(References: example 5 and 6 page 198 - 199, end of section exercises 29 - 34 page 203)
x P(x).. x P(x)... x - (x - )2 P(x) (x - )2
0 0.34.......0..........?...........?........?
1 0.17
2 0.26
3 0.21
4 0.02
x P(x) = P(x) (x - )2 =
(5 points for table)
a. Mean
(2 points)
= 1.596
b. Variance 2
(2 points)
=1.204784
Section 4.2: Binomial Probability
Find the indicated binomial probabilities. Round to the nearest 3 decimal places. (References: example 6 page 212, end of section exercises 15 - 24 page 216 - 217) For part d and e: (References: example 8 page 214)
4. The probability that a pumpkin seed will germinate is 70%. A gardener plants in batches of 12. (1 points each)
a. What is the probability that exactly 10 seeds will germinate?
P(x=10) = 12C10(0.7)^10(0.3)^2 = 66(0.02825)(0.09) = 0.1678
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b. What is the probability that 10 or more will germinate?
P(10<=x<=12) = 0.2528
----------------------------------
c. What is the probability that all seeds will germinate?
P(x=12) = 0.7^12 = 0.0138..
----------------------------------
d. Find the mean
Ans: ?
e. Find the variance 2
Ans: ?
---------------------------------------------
5. A True-False test has 20 questions with each having 2 possible answers with one correct. Assume a student answers every question.
a. What is the probability of getting exactly 9 correct answers?
P(x=9) = 20C9(1/2)^9(1/2)^11 = 167960(1/2^20) = 0.1602
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b. What is the probability of getting less than 6 correct answers?
P(0<= x <= 5) = 0.027
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Cheers,
Stan H.
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