Data were collected from a survey given to graduating college seniors on the number of times they had changed majors. From that data, a probability distribution was constructed. The random variable X is defined as the number of times a graduating senior changed majors. It is shown below: 1 2 4 7 8 P(X = x) 0.253 0.223 0.216 0.199 0.062 0.031 0.011 0.003 0.002 a. What is the probability thata randomly selected student changed his or her major at least once? b. What is the probability that a randomly selected student changed his or her major at most twice? c. What is the probability that a randomly selected student changed his or her major exactly twice? d. What is the mean number of times students changed majors? e. What is the standard deviation of X?
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.
Given random variable X is the number of times a graduating senior changed majors.
The probability distribution of X is as follows ,
a)
We have to find P( student changed major at least once ), i.e P( x 1 )
P( x 1 ) = 1 - P( x < 1 )
P( x 1 ) = 1 - P( x = 0 )
P( x 1 ) = 1 - 0.253
P( x 1 ) = 0.747
b)
We have to find P( student changed major at most twice ), i.e P( x 2 )
P( x 2 ) = P( x =0 )+P( x = 1 ) +P( x =2 )
P( x 2 ) = 0.253 + 0.223 + 0.216
P( x 2 ) = 0.692
c )
We have to find P( student changed major exactly twice ), i. e. P( x = 2 )
P( x = 2 ) = 0.216
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