1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Blababa [14]
3 years ago
8

A study of the pricing accuracy of checkout scanners at a store found that one of every 20 items is priced incorrectly. On any g

iven day, we randomly select five items at a checkout at this store and define X as a variable representing the number of items found to be priced incorrectly by the scanner. a) Assuming that this store sells thousands of items every day, which probability distribution would you use and why? (1 Point) b) What is the probability that exactly one of the five items is priced incorrectly by the scanner? (2 Points) c) What is the probability that at least one of the five items is priced incorrectly by the scanner? (2 Points) Answer.
Mathematics
1 answer:
GalinKa [24]3 years ago
5 0

Answer:

a) There are going to be at least 15 items both priced correctly, and incorrectly, which means that we can use the normal approximation to the binomial to solve the exercise in this supposed problem.

b) 20.36% probability that exactly one of the five items is priced incorrectly by the scanner

c) 22.62% probability that at least one of the five items is priced incorrectly by the scanner

Step-by-step explanation:

For each item, there are only two possible outcomes. Either it is priced correctly, or it is not. The probability of an item being priced incorrectly is independent of other items. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

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

And p is the probability of X happening.

Five items selected.

This means that n = 5

One of 20 is priced incorrectly.

This means that p = \frac{1}{20} = 0.05

a) Assuming that this store sells thousands of items every day, which probability distribution would you use and why?

There are going to be at least 15 items both priced correctly, and incorrectly, which means that we can use the normal approximation to the binomial to solve the exercise in this supposed problem.

b) What is the probability that exactly one of the five items is priced incorrectly by the scanner?

This is P(X = 1).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 1) = C_{5,1}.(0.05)^{1}.(0.95)^{4} = 0.2036

20.36% probability that exactly one of the five items is priced incorrectly by the scanner

c) What is the probability that at least one of the five items is priced incorrectly by the scanner?

Either no items are priced incorrectly, or at least one is. The sum of the probabilities of these events is decimal 1. So

P(X = 0) + P(X \geq 1) = 0

We want P(X \geq 1). So

P(X \geq 1) = 1 - P(X = 0)

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{5,0}.(0.05)^{0}.(0.95)^{5} = 0.7738

P(X \geq 1) = 1 - P(X = 0) = 1 - 0.7738 = 0.2262

22.62% probability that at least one of the five items is priced incorrectly by the scanner

You might be interested in
After examining daily receipts over the past year, it was found that the green parrot italian restaurant has been grossing over
denpristay [2]

Complete question is;

After examining daily receipts over the past year, it was found that the green parrot italian restaurant has been grossing over $2200 a day for about 85% of it's business days. Using this as a reasonably accurate measure, find the probability that the green parrot will gross over $2200:

A. At least 5 of the next 7 business days.

B. at least 5 of the next 10 business days.

C. less than 3 of the next 5 business days.

d. Exactly 7 of the next 10 business days

e. At least 1 of the next 5 business days.

Answer:

A) P(X ≥ 5) = 0.9262

B) P(X ≥ 5) = 0.9986

C) P(X ≤ 2) = 0.0266

D) P(X = 7) = 0.1298

E) P(X ≥ 1) = 0.9999

Step-by-step explanation:

This is a binomial probability distribution problem and as such we will use the formula;

P(X = k) = C(n, k) × p^(k) × (1 - p)^(n - k)

A. At least 5 of the next 7 business days will be;

P (X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7)

P(X = 5) = C(7, 5) × 0.85^(5) × (1 - 0.85)^(7 - 5)

P(X = 5) = 0.20965

P(X = 6) = C(7, 6) × 0.85^(6) × (1 - 0.85)^(7 - 6)

P(X = 6) = 0.396

P(X = 7) = C(7, 7) × 0.85^(7) × (1 - 0.85)^(7 - 7)

P(X = 7) = 0.320577

Thus;

P(X ≥ 5) = 0.20965 + 0.396 + 0.320577

P(X ≥ 5) = 0.9262

B. Probability of at least 5 of the next 10 business days will be;

P(X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

From online binomial calculator attached, we can see that the answer is;

P(X ≥ 5) = 0.9986

C. Probability of less than 3 of the next 5 business days will be;

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

From online binomial calculator attached, we can see that the answer is;

P(X ≤ 2) = 0.0266

D. Probability of exactly 7 of the next 10 business days will be;

P(X = 7) = C(10, 7) × 0.85^(7) × (1 - 0.85)^(10 - 7)

P(X = 7) = 0.1298

e. Probability of at least 1 of the next 5 business days will be;

P(X ≥ 1) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

From third image attached using online binomial calculator, we have;

P(X ≥ 1) = 0.9999

5 0
2 years ago
A circle with radius 4 inches is inscribed in an equilateral triangle. Find the area of the triangle.
LUCKY_DIMON [66]

The inscribed circle has its center at the point of intersection of the angle bisectors, which also happen to be the medians. Hence the altitude of the triangle is 3 times the radius, or 12 inches.

The side length of this triangle is 2/√3 times the altitude, so the area is

... Area = (1/2)·b·h = (1/2)·(24/√3 in)·(12 in)

... Area = 48√3 in² ≈ 83.1384 in²

7 0
3 years ago
Which graph shows a dilation?
Ostrovityanka [42]

Answer:

A

Step-by-step explanation:

Dialation means to get smaller but it has to stay the same shape and measurements tho.

3 0
2 years ago
Item 20
STALIN [3.7K]

Answer:

LLL

Step-by-step explanation:

3 0
3 years ago
The circle has a radius of 11 cm. What is the area of the shaded sector? Use 3.14 for π, and round your answer to the nearest te
Temka [501]
379.9 cm 2 or 253 cm 2
3 0
3 years ago
Other questions:
  • Amanda has a car loan for 12,000 She is paying 3% interest for 6 years. How much will she pay in interest for the 6 years
    13·1 answer
  • I need help with this math work
    11·1 answer
  • At top speed, a rabbit can cover 4 miles in 11 minutes. If a
    12·1 answer
  • A rancher has 400 feet of fencing to put around a rectangular field and then subdivide the field into 2 identical smaller rectan
    15·1 answer
  • verbally explain how to obtain the graph of the quadratic function f(x)=-2(x+3)^2-4 from the graph of y=x^2.
    8·1 answer
  • John is going camping, and he needs to buy a tent. The outdoor store has one that cost $90, but it's on sale for 25% off. What i
    10·2 answers
  • Kylie invested $2,800 in an account paying an interest rate of 5.5 % compounded annually. Ariana invested $2,800 in an account p
    9·1 answer
  • <img src="https://tex.z-dn.net/?f=%5Cfrac%7B-12a%5E%7B3%7Db%20%7D%7B4ab%5E%7B9%7D%20%7D" id="TexFormula1" title="\frac{-12a^{3}b
    7·1 answer
  • Express to the nearest whole
    9·1 answer
  • Sketch the graph of each linear inequality
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!