6The results of a certain medical test are normally distributed with a mean of125 and a standard deviation of 19.(A reading above 113 is considered unhealthy).Use the given table to find the percentage of people with readings above91. z-score-3.0-2.9-2.8-2.7-2.6-2.5-2.4-2.3-2.2-2.1Percentile0.130.190.260.350.470.620.821.071.391.79z-score-2.0-1.9-1.8-1.7-1.6-1.5-1.4-1.3-1.2-1.1Percentile2.282.873.594.465.486.688.089.6811.5113.57z-score-1.0-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.1Percentile15.8718.4121.1924.2027.4330.8534.4638.2142.0746.02 The percentage of people with readings above 91 is _______%.(Round the final answer to the nearest hundredth as needed. Round the z-score to the nearest tenth as needed.)

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Description: 6The results of a certain medical test are normally distributed with a mean of125 and a standard deviation of 19.(A reading above 113 is considered unhealthy).Use the given table to find the percentage of people with readings above91. z-score-3.0

Given: Population mean (μ) = 125 Population standard deviation (σ) = 19 Consider X be the random variable that follows the normal distribution with mean = 125 and standard deviation = 19The percentage of people with readings above 91 is calculated as: PX>91=Px-μσ>91-μσ=PZ>91-12519=P(Z>-1.8)=100%-3.59%=96.41% Thus, the required percentage is 96.41%

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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The results of a certain medical test are normally distributed with a mean of

125 and a standard deviation of 19.

(A reading above 113 is considered unhealthy).

Use the given table to find the percentage of people with readings above

91.

z-score	-3.0	-2.9	-2.8	-2.7	-2.6	-2.5	-2.4	-2.3	-2.2	-2.1
Percentile	0.13	0.19	0.26	0.35	0.47	0.62	0.82	1.07	1.39	1.79
z-score	-2.0	-1.9	-1.8	-1.7	-1.6	-1.5	-1.4	-1.3	-1.2	-1.1
Percentile	2.28	2.87	3.59	4.46	5.48	6.68	8.08	9.68	11.51	13.57
z-score	-1.0	-0.9	-0.8	-0.7	-0.6	-0.5	-0.4	-0.3	-0.2	-0.1
Percentile	15.87	18.41	21.19	24.20	27.43	30.85	34.46	38.21	42.07	46.02

The percentage of people with readings above 91 is _______%.

(Round the final answer to the nearest hundredth as needed. Round the z-score to the nearest tenth as needed.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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