SOLUTION: What percentage is greater than a value that is 1 standard deviation below the mean? (Give your answer correct to the nearest percent.)
A study was conducted to investigate the
Algebra.Com
Question 1192448: What percentage is greater than a value that is 1 standard deviation below the mean? (Give your answer correct to the nearest percent.)
A study was conducted to investigate the relationship between the cost, y (in tens of thousands of dollars), per unit of equipment manufactured and the number of units produced per run, x. The resulting equation for the line of best fit is given below, with x being observed for values between 10 and 200. If a production run was scheduled to produce 50 units, what would you predict the cost per unit to be in dollars?
y hat = 7.7 − 0.06x
$
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
What percentage is greater than a value that is 1 standard deviation below the mean? (Give your answer correct to the nearest percent.)
if the value is 1 standard deviation below the mean, then the z-score is equal to -1.
from the z-score table, area to the left of a z-score of -1 = .15866.
area to the right of that z-score is 1 minus .15866 = .84134.
that means that 84.134% of the area under the normal distribution curve is to the right of a z-score of -1.
the z-score formula is z = (x-m)/s
z is the z-score
x is the raw score, otherwise known as the value in this problem.
m is the mean
s is the standard deviation.
when the z-score is -1, the formula becomes -1 = (x-m)/s.
if you solve for x, you get:
x = -1 * s + m
for example, if the mean is 100 and the standard deviation is 5, the formula becomes:
x = -1 * 5 + 100 = 95.
you have x = 95, m = 100, and s = 5.
you would use the z-score formula to find out what percentage of the scores in a normal distribution are greater than 95 when the mean is 100 and the standard deviation is 5.
you would use the z-score formula to get z = (95 - 100) / 5 = -1.
we already figured out that z-score of -1 has an area of .84135 to the right of it, the example checks out.
if the mean was 100 and the standard deviation was 5, then a value of 95 would have 84.135% of the total possible scores greater than it.
------------------------------------------------------------
A study was conducted to investigate the relationship between the cost, y (in tens of thousands of dollars), per unit of equipment manufactured and the number of units produced per run, x. The resulting equation for the line of best fit is given below, with x being observed for values between 10 and 200. If a production run was scheduled to produce 50 units, what would you predict the cost per unit to be in dollars?
y hat = 7.7 − 0.06x
using this equation, you determine that y-hat = 7.7 - .06 * 50 = 4.7 per unit.
since y-hat represents the cost per unit, then you find that the cost per unit becomes 4.7 when 50 units per run are produced.
your minimum efficiency would be when you produce 10 units per run for a cost per unit of 7.7 - .06 * 10 = 7.1 per unit
.
your maximum efficiency would be when you produce 200 units per run for a cost per unit of 7.7 - .06 * 100 = 1.7 per unit.
RELATED QUESTIONS
A random sample of size 25 is to be selected from a population that has a mean μ =... (answered by Boreal)
A random sample of size 43 is to be selected from a population that has a mean 𝜇 = 55... (answered by CPhill)
The local bakery bakes more than a thousand 1-pound loaves of bread daily, and the... (answered by CPhill)
The local bakery bakes more than a thousand 1-pound loaves of bread daily, and the... (answered by Boreal)
he local bakery bakes more than a thousand 1-pound loaves of bread daily, and the weights (answered by Boreal)
IQ scores in a general adult population have mean 100 and standard deviation 15. A simple (answered by stanbon)
The local bakery bakes more than a thousand 1-pound loaves of bread daily, and the... (answered by ewatrrr)
A random sample of size 34 is to be selected from a population that has a mean μ =... (answered by lynnlo)
3. The weight of pineapple slices, in grams, in a tin is normally distributed with mean... (answered by Boreal)