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?
Z = (score - Mean)/ Standard deviation.
Z = (10 - 21)/10
Look up Z score in table in back of your stat book labeled something like "areas under normal distribution." Since you want it <10, you would be looking for the proportion in the smaller area.
To find the probability that the high temperature X in Columbus, Ohio on January days is less than 10 degrees Fahrenheit, we can use the standard Normal distribution.
The standard Normal distribution has a mean of 0 and a standard deviation of 1. To convert our given Normal distribution with mean 21 and standard deviation 10 to the standard Normal distribution, we need to standardize the value 10.
The formula to standardize a value x of a random variable with mean μ and standard deviation σ is:
z = (x - μ) / σ
In this case, x = 10, μ = 21, and σ = 10. Plugging these values into the formula:
z = (10 - 21) / 10
z = -11 / 10
z = -1.1
Now that we have the standardized value, we can find the corresponding probability using a standard Normal distribution table or a statistical calculator.
Using a standard Normal distribution table, we look up the probability for z = -1.1. The value obtained is 0.1357.
Therefore, P(X < 10) is approximately 0.1357, or 13.57%.