Question 1182320: The average annual salary for all the US teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680. Find that probability that a randomly selected teacher earns between $35,000 and $45,000 a year.
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
x = salary
mu = population mean = 47750
sigma = population standard deviation = 5680
Find the z score for x = 35000
z = (x-mu)/sigma
z = (35000-47750)/5680
z = -2.24 which is approximate
Repeat for x = 45000
z = (x-mu)/sigma
z = (45000-47750)/5680
z = -0.48 which is approximate
Now refer to the Z table in the back of your textbook.
If you don't have your textbook with you, then you can use free online tables such as this one
https://www.ztable.net/
Using a table like that, you should find these approximations
P(Z < -2.24) = 0.01255
P(Z < -0.48) = 0.31561
You should get these values (or close to them) when using any other table. The level of accuracy in the table may vary (depending on the author). Use of a calculator would get you better accuracy. If your teacher insists you use a specific table, then stick to it.
Then we can say
P(a < z < b) = P(z < b) - P(z < a)
P(-2.24 < z < -0.48) = P(z < -0.48) - P(z < -2.24)
P(-2.24 < z < -0.48) = 0.31561 - 0.01255
P(-2.24 < z < -0.48) = 0.30306
P(35000 < x < 45000) = 0.30306
The answer is approximately 0.30306; round this however you need to.
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