Compute the mean and standard deviation for a binomial random variable.
In this section you learned how to compute the mean and standard deviation for a binomial random variable.
Fill in the formulas for the mean and standard deviation of a binomial random variable:
For a binomial distribution: ______________________ and ______________________
You can draw the binomial histograms using StatCrunch. Use ___Stat____, Calculators___________, ______. Fill in the value of n & p from the problem and then enter P( _________ ) before you click “Compute”
What are the 4 shapes that we discussed for histograms back on page 43?
__________________, __________________, _________________, ______________
Fill in the following as you work through your given problems in MyOpenMath.
1. Given: binomial experiment with n = __6_____ and p = _0.12______
a. (Your version might not use all of the cells displayed below)
X 0 1 2 3 4 5 6
P(X) 0.464 0.380 0.130 0.024 0.002 0.000 0.000
b. Make a quick sketch (takes just a few seconds) of the correct histogram.
c. Which of the 4 shapes discussed in this class does this histogram most resemble?
d. _____ = _______________ = ____________ = _________________
Symbol formula with symbols formula with numbers number units
e. __ ___ = _________ _______________ = _____ _____________
Symbol formula with symbols formula with numbers number units
2 Given: binomial experiment with n = ____6___ and p = __0.84_____
a. (Your version might not use all of the cells displayed below)
X 0 1 2 3 4 5 6
P(X) 0.000 0.001 0.007 0.049 0.191 0.401 0.351
b. Make a quick sketch (takes just a few seconds) of the correct histogram.
c. Which of the 4 shapes discussed in this class does this histogram most resemble? ________________
d. __ ___ = __________________ = ___________________ = _________ _____________ Symbol formula with symbols formula with numbers number units
e. = ____________ = = _________ _____________
Symbol formula with symbols formula with numbers number units
3. Given: binomial experiment with n = _______ and p = _______
a. (Your version might not use all of the cells displayed below)
X 0 1 2 3 4 5 6
P(X) 0.016 0.094 0.234 0.313 0.234 0.094 0.016
b. Make a quick sketch (takes just a few seconds) of the correct histogram.
c. Which of the 4 shapes discussed in this class does this histogram most resemble? ___Bell shaped_______________
__ ___ = __________________ = ___________________ = _________ _____________
Symbol formula with symbols formula with numbers number units
___ σ___ = = = ____1____ _____________
Symbol formula with symbols formula with numbers number units
4.In problem 1, p __<__ 0.5 and the shape of the probability histogram was __ ___________________
In problem 2, p __>__ 0.5 and the shape of the probability histogram was ___ __________________
In problem 3, p _=___ 0.5 and the shape of the probability histogram was _ ____________________
This relation is not just true for these binomial histograms. This is true for all binomial histograms.
5.a. rv X = ____________the number of 26 randomly selected people that are
b. Given: binomial experiment with n = _____ and p = ______
c. __ ___ = _________________ = __________________ = ___2______ _____________
Symbol formula with symbols formula with numbers number unit
Interpret the mean in the context of this problem: _ Out of every 26 people, 2.86 of them on average are left-handed
d. σ = _______________ = ___= _________ _____________
Symbol formula with symbols formula with numbers number units
6.a. rv X = _______ the number of 49 randomly selected M&Ms that are brown _________________________________________________________________
b. Given: binomial experiment with n = _______ and p = ______
c. ____ ___ = __________________ = ___________________ = _________ _____________
Symbol formula with symbols formula with numbers number units
Interpret the mean in the context of this problem: __Out of every 49 M&Ms, 6.86 of them on average are brown
d. __ ___ = __________________ = _____________ = ________ _____________
Symbol formula with symbols formula with numbers number units
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