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Statistics Problem Set: Binomial Random Variables

38. Suppose x is a binomial random variable with n = 3 and p = 3
a. calculate the value of p(x), x = 0,1,2,3 using the formula for a binomial probability distribution
b. using your answers to part a, give the probability distribution for x in tabular form

42. The binomial probability distribution is a family of probability distributions with each single distribution depending on the values of n and p. Assume that x is a binomial random variable with n =4.
a. determine a value of p such that the probability distribution of x is symmetric
b. determine a value of p such that the probability distribution of x is skewed to the right
c. determine a value of p such that the probability distribution of x is skewed to the left
d. graph each of the binomial distributions you obtained in parts a, b, c. locate the mean for each distribution on its graph.
e. in general for what values of p will a binomial distribution be symmetric? skewed to the right? skewed to the left?

80. find the are under the standard normal probability distribution between the following pairs of z-scores:
a. z=0 and z=2.00
b. z=0 and z=3
c. z=0 and z=1.5
d. z=0 and z=.80

82. find the following probabilities for the standard normal random variable z:
a. P(-1<z<1)
b. P(-2<z<2)
c. P(-2.16< or =z < or = .55)
d. P(-.42<z<1.96)
e. P(z< or = 2.33)
f. P(z<2.33).

Solution Preview

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38.
I suppose p = 0.3.
a) P(x=0)=3C0*0.3^0*(1-0.3)^3=1*1*0.7^3=0.343
P(x=1)=3C1*0.3^1*(1-0.3)^2=3*0.3*0.7^2=0.441
P(x=2)=3C2*0.3^2*(1-0.3)^1=3*0.3^2*0.7=0.189
P(x=3)=3C3*0.3^3*(1-0.3)^0=1*0.3^3=0.027
b) x 0 1 2 3
P 0.343 0.441 ...

Solution Summary

The solution assists with answering the binomial random variables in the statistics problem set.

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