Mathematics, 05.10.2019 05:20 burnsmykala23

Thirty percent of all customers who enter a department store will make a purchase. suppose that 6 customers enter the store and that these customers make independent purchase decisions. a. find the probability that exactly 5 customers make a purchase b. find that probability that at least 3 customers make a purchase c. find the probability that two or fewer customers make a purchase d. find the probability that at least one customer makes a purchase. e. as the manager of the department store, how should store associates persuade customers who enter the store to make a purchase

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Answer from: ejcastilllo

Step-by-step explanation:

Let's use binomial distribution, because we are interested in find the total number of successes in a sequence of n independent experiments.

In probability, a binomial distribution is used in a Bernoulli process. That is, a sequence of experiments of n independent trials, each asking a dichotomous question, that means it only has two answers. One answer is a success (probability: p) and the other is a failure (probability: 1-p). In this case, every customer who enters in the store is the experiment. If they make a purchase is a success event, taking into account that every purchase decision has to be independent.

$P(X=x) = C(n,x)p^{x} (1-p)^{n-x}$

x= total number of success

n= total number of experiments

p=probability of success on an indivual trial

$C(n,x) = \frac{n!}{x!(n-x)!}$

a) x= 5 ------> customers that make a purchase

n= 6 ------> total customers

p=0.3

$p(X=5)= C(6,5)(0.3)^{5} (1-0.3)^{6-5} \\p(X=5)=0.102$

b) At least 3 customers make a purchase. x ≥ 3

$P(X\geq 3)=1-P (X=0)-P(X=1)-P(X=2)\\P(X\geq 3)=1-(C(6,0)(0.3^{0})(0.7)^{6}) - (C(6,1)(0.3^{1})(0.7)^{5}) - (C(6,2)(0.3^{2})(0.7)^{4})\\ P(X\geq 3) = 1-0.11765-0.30253-0.32414\\P(X\geq3)= 0.2557$

c) At most 2 customers make a purchase. x ≤ 2

$P(X\leq2) = P(X=0) + P(X=1) + P(X=2)\\P(X\leq2) = (C(6,0)(0.3^{0})(0.7)^{6}) + (C(6,1)(0.3^{1})(0.7)^{5}) + (C(6,2)(0.3^{2})(0.7)^{4})\\P(X\leq2) = 0.11765-0.30253-0.32414\\P(X\leq2)=0.7443$

d)At least 1 customer makes a purchase. x ≥ 1

$P(X\geq 1)=1-P(X=0)\\P(X\geq 1)= 1-C(0,6)(0.3)^{0}(0.7)^{6} \\P(X\geq 1)= 1-0.11765 = 0.8824$

e)They must be kind to customers, always willing to help and give information about products clearly and honestly.

Have enough inventory and offer promotions for the purchase of more than one product

Have an agile payment system that avoids rows and delays in purchases.

Answer from: Quest

The correct answer would be the function g(x) increased at a faster rate

Answer from: Quest

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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