Question

Thirty percent of all customers who enter a store will make a purchase. Suppose 10 customers enter the store, and that they make independent purchasing decisions. (a) Let X be the number, out of the 10 customers in the store, who will make a purchase. Write the binomial probability density function for this situation. (b) Use the binomial distribution to calculate the probability exactly 5 customers make a purchase. (c) Find the probability that 4 or fewer customers make a purchase. (d) Find the probability that 7 or more customers make a purchase.

          Thirty percent of all customers who enter a store will make a
purchase.  Suppose 10 customers enter the store, and that they
make independent purchasing decisions.
(a) Let X be the number, out of the 10 customers in the store,
who will make a purchase.  Write the binomial probability
density function for this situation.
(b) Use the binomial distribution to calculate the probability
exactly 5 customers make a purchase.
(c) Find the probability that 4 or fewer customers make a
purchase.
(d) Find the probability that 7 or more customers make a
purchase.
        
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Added by Glenn T.

Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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Thirty percent of all customers who enter a store will make a purchase. Suppose 10 customers enter the store, and that they make independent purchasing decisions. (a) Let X be the number, out of the 10 customers in the store, who will make a purchase. Write the binomial probability density function for this situation. (b) Use the binomial distribution to calculate the probability exactly 5 customers make a purchase. (c) Find the probability that 4 or fewer customers make a purchase. (d) Find the probability that 7 or more customers make a purchase.
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Transcript

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00:01 In this question we are given that number sample size is equal to 10 value of p is given as 0 .30.
00:10 So for the solution of first part we will let here x be the number number out of 10 customers out of 10 customer in this store so as for the question first of all we will write our binomial probability density function so x is similarly equal to binomial 10 .0 .30.
00:47 So for this probability of getting capital x is equal to x is equal to as per the binomial formula and see our 10 by x, then 0 .3 to the power of x, then q which is 1 minus 0 .3 to the power of n minus r.
01:07 So here this will be as 10 minus x.
01:10 And the value of x is here as 0, 1, 2, 3 and so on till 10.
01:20 So here is the binomial expression of the given question and this is our solution for a part of the question.
01:30 Answer for a part.
01:31 Now let's simplify our next part which is part b.
01:34 So in the part b we will use again the binomial distribution distribution for finding exactly 5 custom.
01:55 Customers to make the purchase and that will be calculated probability of getting x is equal to 5 so this is 10 to 5 0 .3 to the power of 5 1 minus 0 .3 to the power of 10 minus 5 and when we compute this this will be equal to 0 .10 to 9 so here's the solution of b part for getting probability exactly five customers.
02:28 This is a solution for b part.
02:31 Answer for b part is here.
02:34 Then in the c part we have to compute here with probability that 4 or fewer customer will make a purchase...
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