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solmaris [256]
3 years ago
6

If you get a sneak peak at the salary list of your job and realize you are in the lowest bracket, which is the lowest 1%, what i

s your salary if you know that the mean salary is $48,000 and it has a standard deviation of $5500?
Mathematics
1 answer:
hoa [83]3 years ago
7 0

Answer:

z=-2.33

And if we solve for a we got

a=48000 -2.33*5500=35185

And for this case the answer would be 35185 the lowest 1% for the salary

Step-by-step explanation:

Let X the random variable that represent the salary, and for this case we can assume that the distribution for X is given by:

X \sim N(48000,5500)  

Where \mu=48000 and \sigma=5500

And we want to find a value a, such that we satisfy this condition:

P(X>a)=0.99   (a)

P(X   (b)

We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.01 of the area on the left and 0.99 of the area on the right it's z=-2.33. On this case P(Z<-2.33)=0.01 and P(z>-2.33)=0.99

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-2.33

And if we solve for a we got

a=48000 -2.33*5500=35185

And for this case the answer would be 35185 the lowest 1% for the salary

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