Answer:
Step-by-step explanation:
Since the number of pages that this new toner can print is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = the number of pages.
µ = mean
σ = standard deviation
From the information given,
µ = 2300 pages
σ = 150 pages
1)
the probability that this toner can print more than 2100 pages is expressed as
P(x > 2100) = 1 - P(x ≤ 2100)
For x = 2100,
z = (2100 - 2300)/150 = - 1.33
Looking at the normal distribution table, the probability corresponding to the z score is 0.092
P(x > 2100) = 1 - 0.092 = 0.908
2) P(x < 2200)
z = (x - µ)/σ/√n
n = 10
z = (2200 - 2300)/150/√10
z = - 100/47.43 = - 2.12
Looking at the normal distribution table, the probability corresponding to the z score is 0.017
P(x < 2200) = 0.017
3) for underperforming toners, the z score corresponding to the probability value of 3%(0.03) is
- 1.88
Therefore,
- 1.88 = (x - 2300)/150
150 × - 1.88 = x - 2300
- 288 = x - 2300
x = - 288 + 2300
x = 2018
The threshold should be
x < 2018 pages
Answer:
9
Step-by-step explanation:
x didn't change in value, y changed by 9
the distance between the two points is 9
Answer:
The minimum percentage of the commuters in the city has a commute time within 2 standard deviations of the mean is 75%.
Step-by-step explanation:
We have no information about the shape of the distribution, so we use Chebyshev's Theorem to solve this question.
Chebyshev Theorem
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by 
.
Applying the Theorem
The minimum percentage of the commuters in the city has a commute time within 2 standard deviations of the mean is 75%.
75,314 because it is only 5 numbers so this is correct.
Say x is the number
7x +3 = 39 -2x
Add 2x to each side
9x +3 =39
Subtract 3 from each side
9x =36
Divide by 9 on each side
x=4
Hope this helped
