(6x -9) + 5= 2
= -54 + 5
= 2
Since the sample is greater than 10, we can approximate this binomial problem with a normal distribution.
First, calculate the z-score:
z = (x - μ) / σ = (37000 - 36000) / 7000 = 0.143
The probability P(x > 37000$) = 1 - P(<span>x < 37000$),
therefore we need to look up at a normal distribution table in order to find
P(z < 0.143) = 0.55567
And
</span>P(x > 37000$) = 1 - <span>0.55567 = 0.44433
Hence, there is a 44.4% probability that </span><span>the sample mean is greater than $37,000.</span>
Corrine earns an hourly wage on top of her weekly gas allowance for her delivery job.
Her weekly earnings can be expressed as:
Earnings = 40 + 7.50h
When h=0, her earnings will be 40
This constant represents, the fixed gas allowance she is receiving for her delivery job. 7.50h represents that she get paid $7.50 for an hour of work.
So, the constant term in the expression represent her weekly gas allowance.
Using the normal distribution, it is found that a student has to score 0.6433 standard deviations above the mean to be publicly recognized.
<h3>Normal Probability Distribution</h3>
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.
The top 26% of the scores are given by scores above the 74th percentile, which corresponds to Z = 0.6433, hence, a student has to score 0.6433 standard deviations above the mean to be publicly recognized.
More can be learned about the normal distribution at brainly.com/question/24663213