Answer:
16% probability that the facility needs to recalibrate their machines.
Step-by-step explanation:
We have to use the Empirical Rule to solve this problem.
Empirical Rule:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
What is the probability that the facility needs to recalibrate their machines?
They will have to recalibrate if the number of defects is more than one standard deviation above the mean.
We know that by the Empirical Rule, 68% of the measures are within 1 standard deviation of the mean. The other 100-68 = 32% is more than 1 standard deviation from the mean. Since the normal distribution is symmetric, of those 32%, 16% are more than one standard deviation below the mean, and 16% are more than one standard deviation above the mean.
So there is a 16% probability that the facility needs to recalibrate their machines.
Answer:
Step-by-step explanation:
We would apply the formula for exponential decay which is expressed as
A = P(1 - r)^t
Where
A represents the value of the car after t years.
t represents the number of years.
P represents the initial value of the car.
r represents rate of decay.
From the information given,
A = $2700
P = $20300
n = 2004 - 1997 = 7 years
Therefore,
20300 = 2700(1 - r)^7
20300/2700 = (1 - r)^7
7.519 = (1 - r)^7
Taking log of both sides, it becomes
Log 7.519 = 7 log(1 - r)
0.876 = 7 log(1 - r)
Log (1 - r) = 0.876/7 = 0.125
Taking inverse log of both sides, it becomes
10^log1 - r = 10^0.125
1 - r = 1.33
r = 1.33 - 1 = 0.33
The expression would be
A = 20300(1 - 0.33)^t
A = 20300(0.67)^t
Therefore, in 2007,
t = 2007 - 1997 = 10 years
The value would be
A = 20300(0.67)^10
A = $370
Answer:
Step-by-step explanation:
<em>Subtract the students who don't have protractors from the students who have mathematical instruments.</em>
Any number times 0 is going to equal 0
Answer:
Interest earned = 2713.8
Explanation:
We will solve this problem on two steps:
1- get the final amount after three years
2- get the interest earned by subtracting the initial amount from the final one.
1- getting the final amount after 3 years:
The formula that we will use is as follows:
A = P (1 + r/n)^(nt)
where:
A is the final amount we want to calculate
P is the initial amount = 6300
r is the interest = 0.12
n is the number of compounds per year =12
t is time in years = 3
Substitute to get the final amount:
A = P (1 + r/n)^(nt)
A = 6300 (1 + 0.12/12) ^ (12*3)
A = 9013.8
2- getting the interest earned:
Interest earned = final amount - initial amount
Interest earned = 9013.8 - 6300
Interest earned = 2713.8
Hope this helps :)
