Download Normal Approximation to the Binomial worksheet

MAT 470, Worksheet 6
Name:_____________________
1. Consider a binomial experiment consisting of 100 trials.
The probability of success on each problem is 0.15.
A portion of the corresponding histogram is shown.
Let X be the number of successes.
a). What is the mean and standard deviation
for this distribution?
b). Determine the following binomial probabilities.
i). P( X = 10 successes ) =
ii). P( X = 15 successes ) =
c). Use the normal distribution to approximate the following binomial probabilities
i). P( X < 20 successes) =
compare with
binomcdf(100,0.15,20) = 0.93368
ii). P( X > 18 successes ) =
compare with
1 - binomcdf(100,0.15,18) = 0.16283
iii). P( 8 < X < 22 successes) =
2. Let X be a normally distributed random variable with mean 60.
Given that P( X < 70) = 0.94, determine the following probabilities:
a). P( X > 70 ) =
b). P( 60 < X < 70 ) =
c). P( X < 60 ) =
d). P( 50 < X < 70 ) =
3. For a binomial experiment with 200 trials and probability of success p = 0.6, determine
the following values.
a). the mean and the standard deviation: = ________,  = _________
b). Using the normal distribution, approximate the probability P( 115 < X < 125 ).
c). Using the normal distribution, approximate the probability P( 110 < X < 130 ).
d). Using the normal distribution, approximate the probability P( X < 130 ).
Note binomcdf(200,0.6,130) = 0.9360974 is the actual cumulative probability.