SOLUTION: I have answered some of these but am not for sure if they are correct, the others, I am not for sure. Thanks in advance 1. Decide whether the random variable is discrete or c

Question 235963: I have answered some of these but am not for sure if they are correct, the others, I am not for sure. Thanks in advance
1. Decide whether the random variable is discrete or continuous.
a.The number of bottles of water drunk in Florida in August 2008
Discrete
b.The number of wasps in the lab test nest
Discrete
c.The height of sophomores in a required US History class at Ridgemont High in 2008
Continuous

d.The number of players on the Washington Redskins
Discrete

e.The speed of cars starting in the Darlington 500 in 2008
Continuous

2. Decide whether the distribution is a probability distribution. If it is not a probability distribution, identify the property that is not satisfied.
x P(x)
1 0.200
2 0.238
3 0.245
4 0.307
No it is not a probability distribution. It does not equal 1.
0.200 + 0.238 + 0.245 + 0.307 = 0.99

Section 4.2: Binomial Probability

4. In a local college, 60% of the math majors are women. Fifteen math majors are chosen at random. (1 points each)
a. What is the probability that exactly 6 are women?
b. What is the probability that 5 or less women are selected?
c. What is the probability that 10 women are selected?

d. Find the mean 
e. Find the variance 2

5. A multiple choice test has 20 questions with each having 4 possible answers with one correct. Assume a student randomly guesses the answer to every question. (2.5 points each)
a. What is the probability of getting exactly 11 correct answers?
b. What is the probability of getting less than 9 correct answers?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. Decide whether the random variable is discrete or continuous.
a.The number of bottles of water drunk in Florida in August 2008
Discrete
OK
-----------------------
b.The number of wasps in the lab test nest
Discrete
OK
-----------------------
c.The height of sophomores in a required US History class at Ridgemont High in 2008
Continuous
OK
-----------------------------
d.The number of players on the Washington Redskins
Discrete
OK
--------------
e.The speed of cars starting in the Darlington 500 in 2008
Continuous
OK
--------------------------
2. Decide whether the distribution is a probability distribution. If it is not a probability distribution, identify the property that is not satisfied.
x P(x)
1 0.200
2 0.238
3 0.245
4 0.307
No it is not a probability distribution. It does not equal 1.
0.200 + 0.238 + 0.245 + 0.307 = 0.99
OK
---------------------
Section 4.2: Binomial Probability
4. In a local college, 60% of the math majors are women. Fifteen math majors are chosen at random. (1 points each)
a. What is the probability that exactly 6 are women?
P(x=6) = 15C6(0.6)^6*(0.4)^9 = binompdf(15,0.6,6)= 0.0612
==========================================
b. What is the probability that 5 or less women are selected?
P(0<= x <= 5) = binomcdf(16,0.6,5) = 0.0338
==========================================
c. What is the probability that 10 women are selected?
P(x=10) = binompdf(15,0.6,10) = 0.1859
==========================================
d. Find the mean
mean = np = 15*0.6 = 9
=========================================
e. Find the variance
variance = npq = 9*0.4 = 3.6
======================================
5. A multiple choice test has 20 questions with each having 4 possible answers with one correct. Assume a student randomly guesses the answer to every question. (2.5 points each)
a. What is the probability of getting exactly 11 correct answers?
binompdf(20,0.25,11) = 0.0030
b. What is the probability of getting less than 9 correct answers?
binomcdf(20,0.25,8) = 0.9591
===================================
Cheers,
Stan H.

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