Please try to answer using excel functions if possible 8. Assuming a normal dist

Question

Please try to answer using excel functions if possible

8. Assuming a normal distribution, compute the following probabilities, use Excel functions and standard mathematical notation. NotationProbability a) Probability that a single person drawn at random has a salary less than $90,000 b) Probability that a single person drawn at random has a salary greater than $100,000 c) Probability that a single person drawn at random has a salary between $80,000 and $110,000 d) Probability that 36 peopole drawn at random have a mean salary less than $90,000

Explanation / Answer

The mean of the given data is-

? = 85666.67

Compute this using average(data) function in excel

Let X be the random variable describing the salary of an individual

And we know that X is normal

For each question we need to calculate the Z- score given by Z = (x-? )/s

s is the standard deviation of this sample given in excel using the stdev.s(data) function

Use norm.dist(x. mean. SD, 1) function and feed respective values to get the probabilities for Z values

Let me know if you need anything else, if not please don't forget to like the answer :)

Notation Z-Score Probability Using Z-table the values 1 P(X<90000) 0.406 P(Z<0.406) 0.6572 2 P(X>100000) 1.344 P(Z>1.344) 0.0901 3 P(80000<X<110000) P(-0.531<Z<2.281) 0.2894 For 80000 -0.531 For 110000 2.281

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