Mathematics, 05.05.2020 15:58 nnekas

A consumer looking to buy a used red Miata car will call dealerships until she finds a dealership that carries the car. She estimates the probability that any independent dealership will have the car will be 28%. We are interested in the number of dealerships she must call.

a. In words, define the Random Variable X.

b. List the values that X may take on.

c. Give the distribution of X. X∼

d. On average, how many dealerships would we expect her to have to call until she finds one that has the car?

e. Find the probability that she must call at most 4 dealerships.

f. Find the probability that she must call 3 or 4 dealerships.

Answers: 3

Show answers

Answers

Answer from: tommyaberman

(a) X = number of dealerships the customer needs to call before she finds a used red Miata car.

(b) X = 1, 2, 3, 4,...

(d) The expected number of dealerships would we expect her to call until she finds one that has the car is 3.57.

(e) The probability that she must call at most 4 dealerships is 0.7313.

(f) The probability that she must call 3 or 4 dealerships is 0.2497.

Step-by-step explanation:

(a)

The random variable X can be defined as the number of dealerships the customer needs to call before she finds a used red Miata car.

(b)

The values that the random variable X can assume are:

X = 1, 2, 3, 4,...

(c)

The random variable X is defined as the number of trials before the first success. Each trial is independent of the others. And each trial has a similar probability of success.

This implies that the random variable X follows a Geometric distribution.

The probability of success, i.e. the probability that any independent dealership will have the car is p = 0.28.

Thus, the distribution of X is, $X\sim Geometric\ (p=0.28)$ .

(d)

The expected value of a Geometric distribution is:

$E(X)=\frac{1}{p}$

Compute the expected number of dealerships would we expect her to call until she finds one that has the car as follows:

$E(X)=\frac{1}{p}$

$=\frac{1}{0.28}\\$

=3.57

Thus, the expected number of dealerships would we expect her to call until she finds one that has the car is 3.57.

(e)

Compute the probability that she must call at most 4 dealerships as follows:

P (X ≤ 4) = P (X = 1) + P (X = 2) + P (X = 3) + P (X = 4)

$=\sum\limits^{4}_{x=1}{(1-0.28)^{x-1}\times 0.28}\\=0.28+0.2016+0.1452+0.1045\\=0.7313$

Thus, the probability that she must call at most 4 dealerships is 0.7313.

(f)

Compute the probability that she must call 3 or 4 dealerships as follows:

P (X = 3 or X = 4) = P (X = 3) + P (X = 4)

$=[(1-0.28)^{2-1}\times 0.28]+[(1-0.28)^{4-1}\times 0.28]\\=0.14515+0.10451\\=0.24966\\\approx0.2497$

Thus, the probability that she must call 3 or 4 dealerships is 0.2497.

Answer from: Quest

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.

Answer from: Quest

55% are girls and 45% are boys : ) hope this

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 18:20

F(n + 1) = f(n) – 8. if f(1) = 100, what is f(6)?

Answers: 1

Answer

Mathematics, 21.06.2019 18:30

Let f(x) = 3 − x . find the average rate of change of f(x) from x = a to x = a + h and simplify your answer so that no single factor of h is left in the denominator.

Answers: 1

Answer

Mathematics, 21.06.2019 19:10

Girardo is using the model below to solve the equation . girardo uses the following steps: step 1 add 4 negative x-tiles to both sides step 2 add 1 negative unit tile to both sides step 3 the solution is which step could be adjusted so that gerardo's final step results in a positive x-value? in step 1, he should have added 4 positive x-tiles to both sides. in step 1, he should have added 3 negative x-tiles to both sides. in step 2, he should have added 4 negative unit tiles to both sides. in step 2, he should have added 1 positive unit tile to both sides.

Answers: 2

Answer

Mathematics, 21.06.2019 21:00

You have 12 balloons to blow up for your birthday party. you blow up 1/3, and your friend blows up 5 of them. what fraction of the baloons still need blowing up

Answers: 1

Answer

You know the right answer?

A consumer looking to buy a used red Miata car will call dealerships until she finds a dealership th...

Questions