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
pychu [463]
3 years ago
6

A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the

true proportion is 0.06. If 235 are sampled, what is the probability that the sample proportion will differ from the population proportion by greater than 0.04
Mathematics
1 answer:
Tresset [83]3 years ago
7 0

Answer:

0.0098 = 0.98% probability that the sample proportion will differ from the population proportion by greater than 0.04

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

Suppose the true proportion is 0.06.

This means that p = 0.06

235 are sampled

This means that n = 235

Mean and standard deviation:

\mu = p = 0.06

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.06*0.94}{235}} = 0.0155

What is the probability that the sample proportion will differ from the population proportion by greater than 0.04?

Proportion below 0.06 - 0.04 = 0.02 or above 0.06 + 0.04 = 0.1. Since the normal distribution is symmetric, these probabilities are equal, which means that we can find one of them and multiply by 2.

Probability the proportion is below 0.02.

p-value of Z when X = 0.02. So

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

By the Central Limit Theorem

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

Z = \frac{0.02 - 0.06}{0.0155}

Z = -2.58

Z = -2.58 has a p-value of 0.0049.

2*0.0049 = 0.0098

0.0098 = 0.98% probability that the sample proportion will differ from the population proportion by greater than 0.04

You might be interested in
A farmer has a sack of grain, a chicken and a fox. He has to get them across the river and he can't go around or fly but he does
snow_tiger [21]
<span>

</span><span>http://www.squiglysplayhouse.com/BrainTeasers/bt.php?id=119
 this should help</span>
7 0
3 years ago
A hotdog is heated to 700° F. The airplane drops the hotdog next to the fire department. How long until the cow eats the roller
bazaltina [42]

Answer:

showers

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What did everyone say after the bumpy airplane landing
Nikitich [7]
<span>the thing that everyone say after the bumpy airplane landing was : it's not the airplane's fault and it's not the pilot's fault so it's probably the asphalt To be fair, there is no way for the passangers to know what may have caused the bump in landing. Everyone only created their own assumptions based om their personal perspective</span>
8 0
3 years ago
Nathan and Steven stacked boxes on a shelf. Nathan lifted 13 boxes and Steven lifted 15 boxes. The boxes that Nathan lifted each
diamong [38]
I would have to go with C.  i might be wrong hope its right if it is rate please

3 0
3 years ago
What is the solution to 2.1m = 6.3? A. m = 8.4 B. m = 3 C. m = 3.2 D. m = 4.2
sdas [7]
\bf \frac{~~2.1m}{2.1} = \frac{6.3}{2.1} \newline \newline m ~=~3
7 0
3 years ago
Other questions:
  • What is product of 3 1/3 * 2 1/6 in its simplest form
    10·2 answers
  • Plz help me!!with this!!
    8·1 answer
  • A recent survey found that 86% of employees plan to devote at least some work time to follow games during the NCAA Men's Basketb
    13·1 answer
  • Least to greatest 2.614;2.146;2.46;2.164
    13·2 answers
  • Loreena is the goalie for her hockey team. During one game, she stopped approximately
    12·2 answers
  • The position of an object along a vertical line is given by s(t) = −t3 + 3t2 + 7t + 4, where s is measured in feet and t is meas
    12·2 answers
  • State the independent variable and the dependent variable in the linear relationship. Then find the rate of change for the situa
    11·1 answer
  • Question 7 A number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome.
    6·1 answer
  • PLEASE HELP ME IF YOU CAN! please tell me how you got the answer thank you!
    12·1 answer
  • What Made Gandhi's Nonviolent Movement Work?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!