The annual salaries of employees in a large company are approximately normally disributed with a mean of $50,000 and a standard deviation of $20,000. a. what percent of people earn less than $40,000? b. what percent of people earn between $45,000 and $65,000? c. what percent of people earn more than $70,000?


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Question Number 97803 by pete last updated on 09/Jun/20

$The annual salaries of employees in a large$ $company are approximately normally$ $disributed with a mean of $ 50, 000 and a standard$ $deviation of $ 20, 000 .$ $a . what percent of people earn less than$ $$ 40, 000 ?$ $b . what percent of people earn between$ $$ 45, 000 and $ 65, 000 ?$ $c . what percent of people earn more than$ $$ 70, 000 ?$
	Answered by Rio Michael last updated on 10/Jun/20

	$(a) for this question, x = 40, 000 and z - value = - 0.5$ $P (x < 40000) take the area of the normal distribution curve$ $to the left of - 0.5 = 0.308 \Rightarrow percentage = 0.308 \times 100 = 30 . 8 %$ $(b) when x = 45000, z = - 0.25 when x = 65000, z = 0.75$ $P (45000 < x < 65000) we need the area of the normal$ $distribution curve inbetween - 0.25 and 0.75 = 0.3720$ $\Rightarrow percentage = 0.3720 \times 100 = 37 . 20 %$ $(c) for x = 70, 000, z = 1$ $P (x > 70000) will be the area of the normal distribution curve$ $to the right of 1 . = 0.1586$ $\Rightarrow percentage = 15 . 86 %$
	Commented by pete last updated on 10/Jun/20

	$Thank u very much sir Rio$
	Commented by Rio Michael last updated on 10/Jun/20

	$You are welcome$
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