37 percent of all customers who enter a store will make a...

37 percent of all customers who enter a store will make a purchase. Suppose that 6 customers enter the store and that these customers make independent purchase decisions. (1) Use the binomial formula to calculate the probability that exactly five customers make a purchase. (Round your answer to 4 decimal places.) (2) Use the binomial formula to calculate the probability that at least three customers make a purchase. (Round your answer to 4 decimal places.) (3) Use the binomial formula to calculate the probability that two or fewer customers make a purchase. (Round your answer to 4 decimal places.) (4) Use the binomial formula to calculate the probability that at least one customer makes a purchase. (Round your answer to 4 decimal places.)

Transcript

00:01 Alright, you're working with binomial probabilities here and asked to use the binomial formula to calculate the following probabilities.

00:07 The binomial formula is going to be found using ncr, where n stands for the number of i'm going to change that formula to x just so that it matches up with what i've already labeled.

00:21 But n stands for the number of trials, x stands for the number of successes, and then you multiply it by p to the x power, which is the number of successes we had, or probability of success, raised to the number of successes we had, times 1 minus p to the n minus x power, or how many failures we had.

00:45 So for number 1, that's pretty straightforward.

00:47 It's just going to equal 6c5 times 0 .37 to the 5th power times 1 minus 0 .37 to the 6 minus 5 power, or 1.

01:05 Now this part right here is just figuring out how many different ways we can get 5 out of, groups of 5 out of 6.

01:15 And most calculators have that capability, any scientific calculator should have that.

01:23 So 6c5 is 6, and then i'm just multiplying by 0 .37 to the 5th power times 0 .63 to the 1st power, and that works out to be 0 .0262.

01:49 Now the way your question was worded, i'm assuming we're not supposed to use any special calculator programs.

01:56 I wouldn't consider this a special calculator program, but there's actually binomial probability calculators that you could use, but i'm assuming we're supposed to not do that because it says using the formula each time.

02:08 So i want to actually skip question number 2, and you'll see that in a minute.

02:12 I'm going to come back to it after i do question number 3.

02:16 For question number 3, i would have to do this formula 3 times, once for x equaling 0, once for x equaling 1, and once for x equaling 2.

02:28 So we'll have 6c0 times 0 .37 to the 0 power, we had no successes, times 0 .63 to the 6th power.

02:44 And then we'll add that to 6c1 times 0 .37 to the 1st power times 0 .63 to the 2nd power, sorry not 2nd power, 5th power for the 5 failures.

03:03 And then one more time, plus 6c2 times 0 .37 to the 2nd power times 0 .63 to the 4th power.

03:16 Now i'm just going to take my time and type all this in and get you a final result.

03:22 I'll be right back.

03:25 And that works out to be 0 .6063...

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