4. Probability computations Ling the standard normal distribution #1 AaAa The av

Question

4. Probability computations Ling the standard normal distribution #1 AaAa The average starting salary offer for information systems majors who graduated in 2007 was $47,soz. [source National Association of colleges and Employers, salary Survey, Fall 2007.] Assume that x, the starting salary offer for information systems majors in the class of '07, is normally distributed with a mean of 47,507 and a standard deviation of $5,000 use the following standard Normal Distribution tool to help you answer the questions that follow Standard Nonmal Distnbution Mean 0.0 Standard Deviation 1.0 2 2 The probability that a randomly selected information systems major from the class of 'o7 received a starting salary offer greater than $52,000 is ermittm The probability that a randomly selected information systems major received a starting salary offer between s45,oo0 and $52,000 is What percentage of information systems majors received a starting offer between $38,o00 and $45,000? 72.02% 018.08% 91.92% 27.98% Twenty percent ot inform ati stems ma were offered a starting salary lass than

Explanation / Answer

Mean = 47507

Sd = 5000

Z = (X - mean) /sd

1) Z score for 52000 = (52000 - 47507)/5000 = 0.9

P(X > 52000) = P(Z > 0.9) = 1 - P(Z < 0.9) = 1 - 0.8159 = 0.1841

2) Z score for 45000 = (45000 - 47507)/5000 = - 0.5

P(45000 < X < 52000) = P(-0.5 < Z < 0.9) = P(Z < 0.9) - P(Z < - 0.5) = 0.8159 - 0.3085 = 0.5074

3) Z score for 38000 = (38000 - 47507)/5000 = - 1.9

P(38000 < X < 45000) = P(-1.9 < Z < - 0.5) = P(Z < - 0.5) - P(Z < - 1.9) = 0.3085 - 0.0287 = 0.2798 = 27.98%

Option-D) 27.98%

D) P(X < x) = 0.2

Or, P(Z < (x-47507)/5000) = 0.2

Or, (x - 47507) / 5000 = - 0.84

Or, x = 47507 - 0.84*5000 = $43307

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