Question

The standard normal distribution is a continuous distribution with a mean of 0 and a standard deviation of 1. The following is true:
About 68% of all outcomes lie within 1 St.Dev.
About 95% of all outcomes lie within 2 St.Devs.
About 99.7% of all outcomes lie within 3 St. Devs.
The probability/percentage/percentile for a normal distribution is the area under the curve. You will ALWAYS BE CALCULATING OVER AN INTERVAL.
Values outside of 2 St.Devs. are considered “unusual values.”
Recall that Zxn=xn-m/ o=value-mean/ st dev. mean=50,000 st deviation=5,000

1.

People who make less than ______________ and more than ______________ are considered unusual

a. $42,000; $58,000 b. $60,000; $40,000 c. $70,000; $30,000 d. $50,000; $70,000 e. $45,000; $55,000

2.

If you were to pick somebody from the company at random, what is the probability that this person makes between $41,000 and $45,000? You may use any method you wish to calculate this.

a. .17 b. .12 c. .07 d. .09 e. .08

3.  About what percent of the company makes more than $55,000?

a. About 10% b. About 16% c. About 22% d. About 30% e. About 84%

4.  About what percent of the company makes less than $42,000?

a. .945 b. .055 c. .033    d. .023 e. .385

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Answer 1

1) The unusual range here are computed as:
Lower limit: Mean - 2* Std Dev = 50000 - 2*5000 = 40000
Upper limit: Mean + 2 STd Dev = 50000 + 2*5000 = 60000

Therefore $60,000; $40,000 are the required values here.

2) The probability here is computed as:

P(41000 < X < 45000)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore b) 0.12 is the required probability here.

3) P(X > 55000) = P(Z > 1)

Getting it from the standard normal tables, we get here:

P(Z > 1) = 0.1587

Therefore b. About 16% is the required probability here.

4) P(X < 42000)

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore b) 0.055 is the required probability here.