4. Management at Gordon Electronics is considering adopting a bonus system to in

Question

4. Management at Gordon Electronics is considering adopting a bonus system to increase production. One suggestion is to pay a bonus on the highest 5 percent of production based on past experience. Past records indicate weekly production follows the normal distribution. The mean of this distribution is 4,000 units per week and the standard deviation is 60 units per week. If the bonus is paid on the upper 5 percent of production, the bonus will be paid on how many units or more? According to a government study among adults in the 25- to 34-year age group, the mean amount spent per year on reading and entertainment is $1,994. Assume that the distribution of the amounts spent follows the normal distribution with a standard deviation of $450 a. What percent of the adults spend more than $2,500 per year on reading and entertainment? b. What percent spend between $2,500 and $3,000 per year on reading and entertainment? c. What percent spend less than $1,000 per year on reading and entertainment?

Explanation / Answer

For any normal random variable X with mean and standard deviation , X ~ Normal( , ), (note that in most textbooks and literature the notation is with the variance, i.e., X ~ Normal( , ² ). Most software denotes the normal with just the standard deviation.)

You can translate into standard normal units by:
Z = ( X - ) /

Where Z ~ Normal( = 0, = 1). You can then use the standard normal cdf tables to get probabilities.

If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed. This is called the Central Limit Theorem.

If a sample of size is is drawn from a population with mean and standard deviation then the sample average xBar is normally distributed

with mean and standard deviation /(n)

An applet for finding the values
http://www-stat.stanford.edu/~naras/jsm/…

calculator
http://stattrek.com/Tables/normal.aspx

how to read the tables
http://rlbroderson.tripod.com/statistics…

In this question we have
X ~ Normal( x = 4000 , x² = 3600 )
X ~ Normal( x = 4000 , x = 60 )

We know that
P(Z > 1.645) = 0.05

so

P( (X - x) / x > 1.645) = 0.05
P( X > x + 1.645) x ) = 0.05
P( X > 4000 + 1.645 * 60 ) = 0.05
P( X > 4098.7) = 0.05

The bonus will be paid to for producing 4098.7 units or more.

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

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