Respuesta :
Mean = 12000
Standard Deviation = 2000
We have to find how many standard deviations is 14,500 away from the mean.
This can be achieved by calculating the z-score
Z-score tells us how many standard deviations above or below is a sample value from the mean. A positive z value shows, sample value is above the mean.
z score can be calculated as = (Sample Value - Mean )/Standard Deviation)
So,
Z-score = [tex] \frac{14500-12000}{2000} =1.25[/tex]
This means, 14,500 is 1.25 standard deviations above the mean value 12,000.
Standard Deviation = 2000
We have to find how many standard deviations is 14,500 away from the mean.
This can be achieved by calculating the z-score
Z-score tells us how many standard deviations above or below is a sample value from the mean. A positive z value shows, sample value is above the mean.
z score can be calculated as = (Sample Value - Mean )/Standard Deviation)
So,
Z-score = [tex] \frac{14500-12000}{2000} =1.25[/tex]
This means, 14,500 is 1.25 standard deviations above the mean value 12,000.
The standard deviation is 1.25 above the mean is 14,500 hours.
Given that
The life of a manufacturer's compact fluorescent light bulbs is normal, with a mean of 12,000 hours and a standard deviation of 2,000 hours.
Seth wants to find the probability that a light bulb he purchased from this manufacturer will last no more than 14,500 hours.
We have to determine
How many standard deviations above the mean are 14,500 hours?
According to the question
The mean for the bulb is 12,000 hours.
The standard deviation for the bulb is 2000 hours.
The sample value is 14500.
To find out how many standard deviations is 14500 mean away from the mean the z value of the mean should be calculated.
What is the z-value?
The z value is a numerical measurement that describes a value related to the mean of a group of values.
The z value is the ratio of the difference of the sample value and means to the standard deviation.
Thus the z value for the given mean is,
[tex]\rm z = \dfrac{x-\mu}{\sigma}\\ \\ z = \dfrac{14500-12000}{2000}\\ \\ z= \dfrac{2500}{2000}\\ \\ z = 1.25[/tex]
Hence, the standard deviation is 1.25 above the mean is 14,500 hours.
To know more about Z-value click the link given below.
https://brainly.com/question/1697710
