Determine whether the random variable is discrete or continuous 1. The number of

Question

Determine whether the random variable is discrete or continuous 1. The number of marbles in a bag. 2. The distance a baseball travels in the air after being hit. 3. The square footage of a house 4. The weight of an airplane. 5. The number of points scored in a basketball game. According to a survey by paint manufacturer, DuPont, 22% of all cars in the United States are red. Suppose 20 cars are randomly selected and the number of red cars are recorded. Round probabilities to 4 decimal places. 6. Explain why this is a binomial experiment. 7. Find and interpret the probability that exactly 6 cars are red. 8. Find and interpret the probability that fewer than 6 cars are red. 9. Find and interpret the probability that at least 6 cars are red. 10. Compute the mean and standard deviation of the binomial random variable

Explanation / Answer

(If the value of variable is lies between some interval and it can take any fraction value within given interval, then this variable is called as continuous random variable and if the value is discrete or it takes only integers, then this variable is called as discrete random variable.

Determine whether the random variable is discrete or continuous.

Answers:

1

Discrete random variable

2

Continuous random variable

3

Continuous random variable

4

Continuous random variable

5

Discrete random variable

Question

We are given, n = 20 and p = 0.22

Here, we have to use binomial distribution.

Formula for binomial distribution probability is given as below:

P(X=x) = nCx*p^x*( 1 – p)^(n – x)

6

This is a binomial experiment, because the output for experiment only gives two results such as red car or other colour car.

7

Here, we have to find P(X=6)

P(X=6) = 20C6*0.22^6 * ( 1 – 0.22)^(20 – 6)

P(X=6) = 38760*0.22^6*0.78^14

P(X=6) = 0.135595192

Required probability = 0.135595192

8

Here, we have to find P(X<6)

P(X<6) = P(X5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)

P(X<6) = 0.73426761

Required probability = 0.7343

(By using binomial table or excel)

9

We have to find P(X6)

P(X6) = 1 – P(X<6)

P(X6) = 1 – 0.73426761

P(X6) = 0.2657324

Required probability = 0.2657

(By using binomial table or excel)

10

Mean =n*p = 20*0.22 = 4.4

Standard deviation = sqrt(npq) = sqrt(20*0.22*0.78)

Standard deviation = sqrt(20*0.22*0.78)

Standard deviation = 1.8525658

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