3. Probabilities for the standard normal distribution Aa Aa The average starting

Question

3. Probabilities for the standard normal distribution Aa Aa The average starting salary offer for management majors who graduated in 2007 was $43,256. [Source: National Association of Colleges and Employers, Salary Survey, Fall 2007. 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 -4 The probability that a randomly selected management major from the class of '07 received a starting salary offer less than $48,600 is The probability that a randomly selected management major received a starting salary offer between $42,000 and $48,600 is What percentage of management majors received a starting offer between $36,000 and $42,000? O 66.6196 O 33.39% O 97.13% o 2.87% Twenty percent of management majors were offered a starting salary less than

Explanation / Answer

The probability that a randomly selected management major from the class of 07 received a strating salary offer less than 48600 is
P(X< 48600) = P(Z < (48600 - 43256)/3150)) = P (Z < 1.6965) = 0.95511

The probability that a randomly selected management major from the class of 07 received a strating salary offer between 42000 and 48600

P(42000 <X< 48600) = P(X < 48600) - P(X < 42000)
                   = P(Z < (48600 - 43256)/3150)) - P(Z < (42000 - 43256)/3150))
                   = P(Z<1.6965) - P(Z < -0.3987) = 0.95511 - 0.34506 = 0.61005

The percentage that a randomly selected management major from the class of 07 received a strating salary offer between 36000 and 42000 is

P(36000 < X < 42000) = P(X < 42000) - P(X < 36000)
                   = P(Z < (42000 - 43256)/3150)) - P(Z < (36000 - 43256)/3150))
                   = P(Z < -0.3987) - P(Z < -2.3035) = 0.34506 - 0.01063 = 0.33443 = 33.4%

Correct answer: option (C)

Tweny percent of management majors were offered a staring salary less than 43256 - 0.8416 * 3150 = 40604.96

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