Based on a survey, annual salaries for benefits managers range from $50,935 to $

Question

Based on a survey, annual salaries for benefits managers range from $50,935 to $79,577. A sample of 30 benefit managers salaries were taken and the mean of the data was $63,000 with a sample standard deviation of $4,000. Assume that the distribution of the annual salaries is bell-shaped and assumes a normal distribution.

1. Determine the percentage of annual salaries between $51,000 and $67,000 using the empirical rule.

2. Determine the percentage of annual salaries less than $55,000 using the empirical rule.

3. Determine the percentage of annual salaries that earned more than $75,000 using the empirical rule

Explanation / Answer

1. Determine the percentage of annual salaries between $51,000 and $67,000 using the empirical rule.

Note that 51000 is 3 standard deviations below the mean.

Note that 67000 is 1 standard deviation above the mean.

By 68-95-99.7 rule,

P(51000<x<67000) = (99.7/2 + 68/2) = 83.85% [ANSWER]

**********************************

2. Determine the percentage of annual salaries less than $55,000 using the empirical rule.

Note that 55000 is 2 standard deviations below the mean.

By 68-95-99.7 rule,

P(x<55000) = (100 - 95)/2 = 2.5% [ANSWER]

***********************************

3. Determine the percentage of annual salaries that earned more than $75,000 using the empirical rule

Note that 75000 is 3 standard deviations above the mean.

By 68-95-99.7 rule,

P(x>75000) = (100 - 99.7)/2 = 0.15% [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse B
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.