The binomial random variable X counts the number of students with no siblings in
ID: 3128689 • Letter: T
Question
The binomial random variable X counts the number of students with no siblings in a random sample of high school seniors, where p = 0.05 of all high school seniors have no siblings. The random variable p = X/n is for the proportion of students with no siblings in the sample. For each student in the sample, are we treating information about siblings as a quantitative or categorical variable? Find the mean and standard deviation of X if the sample consists of n = 50 students. (Round to the nearest tenth.) Find the mean and standard deviation of p if the sample consists of n 50 students. (Round to the nearest hundredth.) Find the mean and standard deviation of X if the sample consists of n = 400 students. (Round to the nearest tenth.) In which case is the distribution of X approximately normal-for samples of 50, 400, both, or neither?Explanation / Answer
a. The information regarding sibblings is treated as a categorial variable, as it is clearly seen that X is a random variable who are students with no sibblings
b.clearly, X= 150*.06 =9
c. p cap = X/n =(200/8)=25
d..Mean = n*p =50*.05 =2.5
std deviation = n*p*(1-p) = 2.4
e ..Mean = n*p =50*.05 =2.5
std deviation = n*p*(1-p) = 2.38
f. ..Mean = n*p =400*.05 =20.0
std deviation = n*p*(1-p) = 19.0
g. ..Mean = n*p =400*.05 =20.0
std deviation = n*p*(1-p) = 19.0
h. it is approximately normal for case of 400 observations
i. The probability distribution of X is very much towards the right of curve.
Mean shifts towards right
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