Question

In a particular retail clothing store, approximately 30% of potential customers who walk into the store make a purchase.

In a random sample of 25 customers that walked into the store,

a. what is the probability that exactly 10 of the customers make purchases?

Round to 3 significant digits.

b. what is the probability that at least 2 of the customers make purchases?

Round to 3 significant digits.

c. how many of the customers are expected to make purchases?

Round to 3 significant digits.

d. what is the standard deviation of the number of customers who make purchases?

Round to 3 significant digits.

please provide correct answer.

Answer 1

Solution:

a)

P( 10) = 0.092 ( Round to 3 significant digits )

b)

Pr(X≥2)=P(2)+P(3)+P(4)+P(5)+P(6)+P(7)+P(8)+P(9)+P(10)+P(11)+P(12)+P(13)+P(14)+P(15)+P(16)+P(17)+P(18)+P(19)+P(20)+P(21)+P(22)+P(23)+P(24)+P(25)P(2)+P(3)+P(4)+P(5)+P(6)+P(7)+P(8)+P(9)+P(10)+P(11)+P(12)+P(13)+P(14)+P(15)+P(16)+P(17)+P(18)+P(19)+P(20)+P(21)+P(22)+P(23)+P(24)+P(25)

=0.0074+0.0243+0.0572+0.103+0.1472+0.1712+0.1651+0.1336+0.0916+0.0536+0.0268+0.0115+0.0042+0.0013+0.0004+0.0001+0+0+0+0+0+0+0+0

= 0.998

which means that the probability we are looking for is Pr(X≥2)=0.998

c)  the customers are expected to make purchases

Mean μ=n⋅p=(25) * 0.3 = 7.5

d)