The random variable X represents the number of cars per household in a town of1000 households along with the corresponding probabilities.234Probabilit0.125 0.428 0.256 0.108 0.083y of Xa. Verify that probability distribution for the random variable X is valid.b. Calculate the expected value of X.c. What is the probability that X < 2? The scores out of 50 points on a recent vocabulary test for all of the 120 studentsenrolled in a statistics class at a local high school is approximately normallydistributed with a mean of 34.82 points and a standard deviation of 5.02 points. Theteacher plans to select a random sample of 6 students to survey about how toincrease student performance on the next vocabulary test.a. Calculate the mean and standard deviation of the sampling distribution of X, the= 6.sample mean number of points scored by students for samples of size n =b. Interpret the standard deviation of the sampling distribution calculated in part (a).c. The teacher believes that if a student scored less than 30 points, the student willhave a different opinion than if a student scored more than 30 points. Calculate theprobability that in a random sample of 6 students, the sample average would be lessthan 30 points.

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0 1 4 Probabilit 0.125 0.428 0.256 0.108 0.083 y of X rify that probability distribution for the random variable X is valid. alculate the expected value of X. hat is the nrohability that X < 2? 2.

MATLAB: An Introduction with Applications

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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

The random variable X represents the number of cars per household in a town of
1000 households along with the corresponding probabilities.
2
3
4
Probabilit
0.125 0.428 0.256 0.108 0.083
y of X
a. Verify that probability distribution for the random variable X is valid.
b. Calculate the expected value of X.
c. What is the probability that X < 2?

The scores out of 50 points on a recent vocabulary test for all of the 120 students
enrolled in a statistics class at a local high school is approximately normally
distributed with a mean of 34.82 points and a standard deviation of 5.02 points. The
teacher plans to select a random sample of 6 students to survey about how to
increase student performance on the next vocabulary test.
a. Calculate the mean and standard deviation of the sampling distribution of X, the
= 6.
sample mean number of points scored by students for samples of size n =
b. Interpret the standard deviation of the sampling distribution calculated in part (a).
c. The teacher believes that if a student scored less than 30 points, the student will
have a different opinion than if a student scored more than 30 points. Calculate the
probability that in a random sample of 6 students, the sample average would be less
than 30 points.

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