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creativ13 [48]
3 years ago
15

It is known that 70% of the customers in a sporting goods store purchase a pair of running shoes. a random sample of 25 customer

s is selected. assume that customers' purchases are made independently, and let x represent number of customers who purchase running shoes. find the probability distribution of x.
Mathematics
1 answer:
NikAS [45]3 years ago
8 0

Let x be the discrete random variable whose value is the number of successes in n trials.

The probability distribution function for x of the binomial distribution B(n,p) is defined as

B(n,p)= nC_xp^x(1-p)^{n-x}

Given that the random sample size is n=25

let x represent number of customers who purchase running shoes

Let "p" be the probability of customers in a sporting goods store purchase a pair of running shoes.

It is given that 70% of the customers in a sporting goods store purchase a pair of running shoes.

Thus p=\frac{70}{100}=0.7

Thus the Probability distribution of x is given by

P(X=x)= 25C_x(0.7)^x(1-0.7)^{25-x}, where x=0,1,2,3,...,25.

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