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?
These are the answers that I get to chose from.
A. 0.7433.
B. 0.8643.
C. 0.1357.
D. 0.
To find the probability P(X < 10), where X is the high temperature on January days in Columbus, Ohio, we need to standardize the value of 10 using the mean and the standard deviation.
First, we'll calculate the z-score, which measures the number of standard deviations a particular value is from the mean:
z = (x - μ) / σ
Here, x is the value we want to standardize (10), μ is the mean (21), and σ is the standard deviation (10).
z = (10 - 21) / 10
z = -11 / 10
z = -1.1
Next, we'll use a standard normal distribution table or a calculator to find the probability corresponding to the z-score of -1.1.
P(Z < -1.1) = 0.1357
Since the Normal distribution is symmetric, the probability P(X < 10) is equal to the probability P(Z < -1.1).
Hence, P(X < 10) ≈ 0.1357
Therefore, the probability that the high temperature in Columbus, Ohio on a January day is less than 10 degrees Fahrenheit is approximately 0.1357.