Sam 'vandelay' johnson plays basketball for his college team. you've observed that the probability of sam making a given shot is 0.5 and that the success of a given shot is independent of other shots. over the course of many games, sam takes 100 attempted shots at the basket. let w be the random variable that is the number of successful shots. you should use the normal approximation to the binomial to calculate the probabilities in parts b) and c). give your answers as decimals to 4 decimal places. a) find the probability that sam makes exactly 62 successful shots from the 90 attempts. p(w 62) b) find the probability that sam makes at most 62 successful shots from the 90 attempts. p(w s 62) c) find the probability that sam makes between 50 and 60 successful shots from the 90 attempts. p(50 s w s 60)

a)

b)

c)

Step-by-step explanation:

1) Previous concepts

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".

Solution to the problem

Let W the random variable of interest, on this case we now that:

The probability mass function for the Binomial distribution is given as:

Where (nCx) means combinatory and it's given by this formula:

Part a

For this case we want this probability:

Part b

We need to check the conditions in order to use the normal approximation.

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

And we can use the z score given by this formula:

Part c

For this case we want this probability: