M Chapter 5 d, | eztomheducation.corn hrn.tpx H: Apps. Lenovo a AmazonBrowserear
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M Chapter 5 d, | eztomheducation.corn hrn.tpx H: Apps. Lenovo a AmazonBrowserear @My Lab. Mastering -Lecture Ready 3w Tennessee State Unn ®Informative Essay D. 26 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.) .005231 zy use the binomial formula to calculate the probablity that at least three customers make a purchase Round your answer to 4 decimal places.) Probability o) use the binomial tormuta to calculate the probablly that two or tewer customers make a purchase (Round your answer to 4 decimal places) Probability (4 use the binomia formula to cacniate tblly a at leastone customer makes a purchase. (Round your answer to 4 decimal places) Probability O Type here to searchExplanation / Answer
Solution:
From the given information
The number of customers enter the store n = 6
The percentage of customer enter the store p = 0.26
The pmf of binomial distribution is defined as follows:
P(X=x) = nCx px (1-p)n-x ;x = 0,1,2......,n
=> P(X=x) = 6Cx (0.26)x (1-0.26)6-x ;x = 0,1,2......,n
1) P(X =5) = 6C5 (0.26)5 (1-0.26)6-5 = 0.0052
2) P(X 3) = 1- P( X <3)
= 1-[P(X=0) + P(X = 1) + P(X =2) ]
= 1-[6C0 (0.26)0 (1-0.26)6-0+ 6C1 (0.26)1 (1-0.26)6-1+ 6C2 (0.26)2 (1-0.26)6-2]
= 1-[0.1642+ 0.3462+ 0.3041]
= 0.1855
3) P(X 2) = P(X=0) + P(X = 1) + P(X =2)
= 6C0 (0.26)0 (1-0.26)6-0+ 6C1 (0.26)1 (1-0.26)6-1+ 6C2 (0.26)2 (1-0.26)6-2
= 0.1642+ 0.3462+ 0.3041
= 0.8145
4) P(X 1) = 1- P(X <1)
= 1-P(X = 0)
= 1- 6C0 (0.26)0 (1-0.26)6-0
= 1- 0.1642 = 0.8358
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