Fc 2 Aa 2. Probability computations using the standard normal distribution Aa Th

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Fc 2

Aa 2. Probability computations using the standard normal distribution Aa The average starting salary offer for management majors who graduated in 2007 was $43,256. [Source: Nationa Association of Colleges and Employers, Salary Survey, Fall 2007.1 Assume that x, the starting salary offer for management majors in the class of '07, is normally distributed with a mean of $43, 256 and a standard deviation of $3,150. Use the following Distributions tool to help you answer the questions. Standard Normal Distribution Mean 0.0 Standard Deviation 1.0 The probability that a randomly selected management major from the class of '07 received a starting salary offer less than $42,000 is The probability that a randomly selected management major received a starting salary offer between $42,000 and $48,600 is

Explanation / Answer

Here it is given that sample is normally distributed with mean=43256 and sd=3150

a. We need to find P(x<42000), as it is normally distributed we will convert x to z,

z=x-mean/sd=42000-43256/3150=-0.399

So we need to find P(z<-0.399)=0.5+P(0<z<-0.399)=0.5-0.1551=0.3449

b. Here we need to find P(42000<x<48600), converting x to z we get P(-0.399<z<48600-43256/3150)=P(-0.399<z<1.70)=P(0<z<1.70)-P(0<z<-0.399)=0.4554+0.1551=0.6105

c. Now first we will find P(36000<z<42000), converting this to z we get P(36000-43256/3150<z<-0.4)=P(0<z<-0.4)-P(0<z<-2.3)=-0.1554+0.4893=0.3339

So it is 33.39% of mangement major receives a starting offer between 36000 to 42000

d. Here we need to find P(X<x)=0.20

Using standard normal table we get P(Z<z)=0.20 for z=-0.841

Now z=x-mean/sd=-0.841

So x=-0.841*3150+43256=40606.85

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