A recent survey of Fortune 500 firms found that on average,they contribute $332.54 per month for each salaried employee's health insurance.If you are told that almost all salaried employees at Fortune 500 firms receive a health insurance contribution between $220.61 and $444.47,and assuming a bell-shaped distribution,what must the standard deviation for this data be?

Question

Quizplus · Accepted Answer

According to the information provided, the mean contribution per employee is $332.54. We can set up the following equation:

$444.47 - $332.54 = z * SD

where z corresponds to the number of standard deviations the $444.47 value is from the mean, and SD is the standard deviation we want to find.

Similarly, we can set up another equation for the $220.61 value:

$332.54 - $220.61 = -z * SD

where z is the number of standard deviations the $220.61 value is from the mean.

We can solve this system of equations for SD:

$111.93 = 2z * SD

SD = $111.93 / (2z)

Since we're assuming a bell-shaped distribution, we know that about 95% of the data falls within 2 standard deviations of the mean. In other words, z = 2.

Plugging this into the equation above, we get:

SD = $111.93 / (2*2) = $27.98

Therefore, the standard deviation for this data must be $27.98 or about $28. Rounded to the nearest cent, this corresponds to choice C ($55.98).

A Recent Survey of Fortune 500 Firms Found That on Average,they