The life of a manufacturer's compact fluorescent light bulbs is normal, with mean 12,000 hours and standard deviation 2,000 hour
2 answers:
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 =
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 =
This means, 14,500 is 1.25 standard deviations above the mean value 12,000.
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Answer:
a)
b)
3,814,698
c)
16.08 weeks
Step-by-step explanation:
a)
The question presented here is similar to a compound interest problem. We are informed that there are 400 rice weevils at the beginning of the study. In a compound interest problem this value would be our Principal.
P = 400
Moreover, the population is expected to grow at a rate of 150% every week. This is equivalent to a rate of interest in a compound interest problem.
r = 150% = 1.5
The compound interest formula is given as;
We let y be the weevil population in any given week x. The formula that can be used to predict the weevil population is thus;
b)
The weevil population 10 weeks after the beginning of the study is simply the value of y when x = 10. We substitute x with 10 in the equation obtained from a) above;
Therefore, the weevil population 10 weeks after the beginning of the study is approximately 3,814,698
c)
We are simply required to determine the value of x when y is
1,000,000,000
Substitute y with 1,000,000,000 in the equation obtained in a) above and solve for x;