On her way to work, Mrs. Larsen gets a green light at a certain traffic light only 30% of the time. She wants to find the probab
ility that she will get a green light at this traffic light all five mornings that she travels to work next week. Use the following randomly generated list of 200 five-digit numbers to answer the questions and find the probability.
Select the digits you will use to represent a favorable outcome.
How many favorable outcomes are on this list? What are they?
Given this simulation, what is the probability that Mrs. Larsen will get a green light at this traffic light all five mornings next week?
Select the digits you will use to represent a favorable outcome.
How many favorable outcomes are on this list? What are they?
Given this simulation, what is the probability that Mrs. Larsen will get a green light at this traffic light all five mornings next week?
1 answer:
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Using the <u>normal distribution and the central limit theorem</u>, it is found that there is a 0.1635 = 16.35% probability of a sample result with 68% or fewer returns prior to the third day.
In a normal distribution with mean and standard deviation
, the z-score of a measure X is given by:
- 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 a proportion p in a sample of size n, the sampling distribution of sample proportions has mean
and standard error
In this problem:
- Sample of 500 customers, hence
.
- Amazon believes that the proportion is of 70%, hence
The <u>mean and the standard error</u> are given by:
The probability is the <u>p-value of Z when X = 0.68</u>, hence:
By the Central Limit Theorem
has a p-value of 0.1635.
0.1635 = 16.35% probability of a sample result with 68% or fewer returns prior to the third day.
A similar problem is given at brainly.com/question/25735688