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
iragen [17]
2 years ago
12

Halloween Candy Halloween is Kelly's favorite holiday of the year! Based on experience, Kelly knows that on average, each house

gives him about 4 candies with a standard deviation of 1.5 candies. Each year Kelly visits 35 random houses in his neighborhood. Let X be the total number of candies Kelly will receive from his visits. Last Halloween, Kelly got 122 candies. Approximate the probability that the total number of candies Kelly will receive this year is smaller than last year.
Mathematics
1 answer:
LuckyWell [14K]2 years ago
6 0

Using the <u>normal distribution and the central limit theorem</u>, it is found that there is an approximately 0% probability that the total number of candies Kelly will receive this year is smaller than last year.

Normal Probability Distribution

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.  
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
  • By the Central Limit Theorem, for n instances of a normal variable, the mean is n\mu while the standard deviation is s = \sigma\sqrt{n}.

In this problem:

  • Mean of 4 candies, hence \mu = 4.
  • Standard deviation of 1.5 candies, hence \sigma = 1.5.
  • She visited 35 houses, hence n = 35, \mu = 35(4) = 140, s = 1.5\sqrt{4} = 3

The probability is the <u>p-value of Z when X = 122</u>, hence:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{122 - 140}{3}

Z = -6

Z = -6 has a p-value of 0.

Approximately 0% probability that the total number of candies Kelly will receive this year is smaller than last year.

A similar problem is given at brainly.com/question/24663213

You might be interested in
There are 65 pens in 3 boxes. How many pens are in 12 boxes?
Rainbow [258]

Answer:

260

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
What is the area of this parallelogram?<br><br><br> 104 m²<br><br> 88 m²<br><br> 56 m²<br><br> 32 m²
iragen [17]

Answer: To find area of a rectangle, multiply its base (length) by its height (width). Plug in the base, 7 meters, and the height, 8 meters. So the area of Rectangle DFBE is 56 square meters.

88m

HOPE THIS HELPS

6 0
3 years ago
Laura drives a garbage truck that weighs 3 tons. She picked up 2 tons of recyclables. What is the total weight in pounds of the
Allushta [10]

Answer:

Step-by-step explanation:

Total weight=The garbage truck weight + recyclables weight =3 tons + 2 tons = 5 tons

3 0
3 years ago
Read 2 more answers
Inverse function of y = 3x​
andrey2020 [161]

Answer:

f-1(x) = 1/3x would be the answer

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Which graph represents a function with the initial value of 1/2<br><br> Graph 2
viktelen [127]
Graph 2 because It’s looks like it’s 1/2
5 0
3 years ago
Other questions:
  • Solve the equation <br> -x^2+50=25
    9·2 answers
  • Which step is it?? Please help me.
    6·1 answer
  • leah wants to determine how many poundsare in 2,864 ounces. She creates the equation16x=2,864 to find the answer.Which operation
    7·2 answers
  • What can I learn in finding the sum of consecutive numbers?
    13·1 answer
  • Wha is the name of the line that you use to define a parabola?
    12·2 answers
  • Dinner plates in a restaurant are arranged on 5 shelves, with 48 plates on each shelf. How many dinner plates are on each shelve
    8·1 answer
  • 20. What is the y-intercept of the line<br> y + 11 = -2(x + 1.5).
    8·2 answers
  • 1. Ricky Shu earns a regular hourly rate of $10.50. How much would he earn in 5 days if he worked 5 hours a day?
    10·2 answers
  • Determine whether each figure creates the conditions to form a unique triangle, more than one triangle, or no triangle. Angle me
    10·1 answer
  • What is the answer I need help!
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!