The high temperature X (in degrees Fahrenheit) on January days in Columbus, Ohio varies according to the Normal distribution with mean 21 and standard deviation 10.
The value of P(X < 10) is
http://davidmlane.com/hyperstat/z_table.html
I added the mean of 21 and SD of 10 and the probability is 0.9715. That is not one of my options, please help!
These are my options.
A.0.30
B.0.40
C.0.60
D.0.90
Well, it must be immediately obvious that .9715 is bogus. A score of 10 is more than a whole SD below the mean, so there is no way that P(x<10) > 1/2
When I plugged in the data, I got P(x<10) = 0.1357
Still not one of your choices. However, the closest is 0.3, since you know that the score is well below the mean.
There's a typo somewhere in the problem or the answers.
I get
.30 = P(x<15 or x>26)
...
.90 = P(x<33 or x>8)
To find the value of P(X < 10), we need to calculate the probability of obtaining a temperature less than 10 degrees Fahrenheit from the normal distribution with a mean of 21 and a standard deviation of 10.
To calculate this probability, we can use the standard normal distribution, also known as the Z-distribution. We need to standardize the value of 10 degrees Fahrenheit to a Z-score.
The formula to standardize a value using the Z-score is:
Z = (X - μ) / σ
Where:
Z is the Z-score.
X is the value we want to standardize.
μ is the mean of the distribution.
σ is the standard deviation of the distribution.
Plugging in the values for X, μ, and σ, we get:
Z = (10 - 21) / 10
Z = -11 / 10
Z = -1.1
Now, we can use a standard normal distribution table or a calculator to find the probability associated with Z = -1.1 These tables or calculators provide the cumulative probability from the left-hand side of the distribution curve.
Consulting the standard normal distribution table or using a calculator, we find that the cumulative probability for Z = -1.1 is approximately 0.1357.
Therefore, the value of P(X < 10) is approximately 0.1357 or 13.57%.