Question

In: Statistics and Probability

1. David's gasoline station offers a discount if the customer pays in cash. Past evidence indicates...

1. David's gasoline station offers a discount if the customer pays in cash. Past evidence indicates that 70% of all customers pay in cash (probability of a success). If 10 customers are randomly selected, what is the mean number of customers that pay in cash? Select one:

a. 1.000

b. 0.7

c. 10

d. 7

2. David's gasoline station offers a discount if the customer pays in cash. Past evidence indicates that 70% of all customers pay in cash (probability of a success). If 10 customers are randomly selected, what is the standard deviation of the customer that pay in cash?

Select one:

a. 1.000

b. 0.976

c. 0.028

d. 1.449

3. David's gasoline station offers a discount if the customer pays in cash. Past evidence indicates that 70% of all customers pay in cash (probability of a success). If 10 customers are randomly selected, what is the probability that at least 9 pay in cash?

Select one:

a. 0.033

b. 0.976

c. 0.024

d. 0.149

4. David's gasoline station offers a discount if the customer pays in cash. Past evidence indicates that 70% of all customers pay in cash (probability of a success). If 10 customers are randomly selected, what is the probability that all 10 pay in cash?

Select one:

a. 0.976

b. 0.028

c. 1.000

d. 0.149

5. David's gasoline station offers a discount if the customer pays in cash. Past evidence indicates that 70% of all customers pay in cash (probability of a success). If 10 customers are randomly selected, what is the probability that more than 7 and less than 10 customers pay in cash?

Select one:

a. 0.121

b. 0.354

c. 0.233

d. 0.562

Solutions

Expert Solution

Let X be the number of customer pays in cash in the 10 randomly selected customers.

We know 70% of all customers pay in cash (probability of a success =0.7)

Then X has Binomial distribution with parameters n=10 and p=0.7.

So the probability mass function can be written as

Its mean and variance are given by

______

(1) Answer is d. 7

The mean number of customers that pay in cash ,

(2) Answer is d. 1.449

The standard deviation of the customer that pay in cash

(3).Answer is d. 0.149

the probability that at least 9 pay in cash is

(4) Answer is b. 0.028

the probability that all 10 pay in cash is

(5) Answer is b.0.354

the probability that more than 7 and less than 10 customers pay in cash

orchestra answered 1 year ago

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