300 grams = 0.3 kilograms
Answer:
0.8185 or 81.85%
Step-by-step explanation:
The mean length (μ) of an adult foot is 11 and the standard deviation (σ) is 1.5.
The z score is a measure in statistic used to determine the amount of standard deviation by which the raw score (x) is above or below the mean. If the raw score is above the mean, the z score is positive and if the raw score is below the mean the z sore is negative. It is given by:
![z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
To calculate the probability that a randomly selected male will have a foot length between 8 and 12.5 inches, we first calculate the z score for 8 inches and then for 12.5 inches.
For 8 inches:
![z=\frac{x-\mu}{\sigma}=\frac{8-11}{1.5}=-2](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3D%5Cfrac%7B8-11%7D%7B1.5%7D%3D-2)
For 12.5 inches:
![z=\frac{x-\mu}{\sigma}=\frac{12.5-11}{1.5}=1](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D%3D%5Cfrac%7B12.5-11%7D%7B1.5%7D%3D1)
From the normal distribution table, The probability that a randomly selected male will have a foot length between 8 and 12.5 inches = P(8 < x < 12.5) = P(-2 < z < 1) = P(z < 1) - P(z < -2) = 0.8413 - 0.0228 = 0.8185 = 81.85%
Answer:
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Answer:
The value of the test statistic is of 0.22.
Step-by-step explanation:
Our test statistic is:
![t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
In which X is the sample mean,
is the expected mean,
is the standard deviation(square root of the variance) and n is the size of the sample.
A lumber company is making boards that are 2920.0 millimeters tall.
This means that
.
A sample of 12 is made, and it is found that they have a mean of 2922.7 millimeters with a variance of 121.00.
This means that
. So
![t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%7D)
![t = \frac{2922.7 - 2922}{\frac{11}{\sqrt{12}}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B2922.7%20-%202922%7D%7B%5Cfrac%7B11%7D%7B%5Csqrt%7B12%7D%7D%7D)
![t = 0.22](https://tex.z-dn.net/?f=t%20%3D%200.22)
The value of the test statistic is of 0.22.