Answer:
a) The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Let X the random variable of interest, on this case we know that:
b)
c) For this case we can use the following excel code:
"=BINOM.DIST(60,80,0.613,FALSE)"
And we got 0.00355
d)
And we can use the following excel code:
"=1-BINOM.DIST(50,80,0.613,TRUE)"
And we got 0.3718
Step-by-step explanation:
Assuming the following questions:
a) What is the probability distirbution for X?
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
Let X the random variable of interest, on this case we know that:
b) Using formula calculate the mean and standard deviation of X
By properties we have:
c) Use your calculator to find the probability that DeAndre scored with 60 of these shots
For this case we can use the following excel code:
"=BINOM.DIST(60,80,0.613,FALSE)"
And we got 0.00355
d) Find the probability that DeAndre scores with more than 50 of these shots
We want this probability:
And we can use the following excel code:
"=1-BINOM.DIST(50,80,0.613,TRUE)"
And we got 0.3718