SOLUTION: Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly s
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Question 1207169: Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P17, the 17-percentile. This is the temperature reading separating the bottom 17% from the top 83%.
P17 =
°C
distribution of values is normal with a mean of 167.9 and a standard deviation of 82.
Find P84, which is the score separating the bottom 84% from the top 16%.
P84 =
Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.4-in and a standard deviation of 0.8-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 0.5% or largest 0.5%.
What is the minimum head breadth that will fit the clientele?
min =
What is the maximum head breadth that will fit the clientele?
max =
Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Here is the full question:
Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z > d) = 0.9926, find d.
d =
You can put this solution on YOUR website! Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P17, the 17-percentile. This is the temperature reading separating the bottom 17% from the top 83%.
you are looking for a z-score that have .17 area to the left of it and .83 area to the right of it.
the z-score that has area of .17 to the left of it is equal to -.954.
that same z-score will have an area to the right of it of .83.
distribution of values is normal with a mean of 167.9 and a standard deviation of 82.
Find P84, which is the score separating the bottom 84% from the top 16%.
z-score formula results are shown below.
to find the raw score, use the z-score formula.
when the mean is 167.9 and the standard deviation is 82, the raw score associated with a z-score of .994 is calculated as follows:
z = (x-m)/s becomes .994 = (x-167.9) / 82.
solve for x to get x = .994 * 82 + 167.9 = 249.498.
the probability of getting a raw score less than that is .84 and the probability of getting a raw score greater than that is .16.
Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 6.4-in and a standard deviation of 0.8-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 0.5% or largest 0.5%.
your confidence interval is .99.
that leave .005 area to the left of the confidence interval and .005 area to the right of the confidence interval.
.005 is equivalent to .5%.
.5% on the left and right of the confidence total 1% which is equal to .01.
the confidence interval is therefore equal to 99% of the area under the normal distribution curve, which is equal to .99.
the critical z-scores at .99 confidence interval are plus or minus 2.576 as shown in the following calculator results.
the raw scores are found using the z-score formula as shown below.
when z = plus or minus 2.576 and mean = 6.4 and standard deviation = .8, you get:
minimum z-score = -2.576 = (x - 6.4) / .8.
solve for x to get x = -2.576 * .8 + 6.4 = 4.3392.
that's the minimum head breadth.
maximum z-score = 2.576 = (x - 6.4) / .8.
solve for x to get x = 2.576 * .8 + 6.4 = 8.4608.
that's the maximum head breadth.
here's what it looks like on a z-score calculator.
Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Here is the full question:
Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1. If P(z > d) = 0.9926, find d.
d =
this was answered previously.
the answer was d = -2.437.
that's the z-score that has .9926 of the area under the normal distribution curve to the right of it.
