Question

Suppose X is normally distributed with mean of 15 and standard deviation of 3: X~N(15, 32). Please get the following probabilities. (Details are required)

1). P(X< 18.3) =

---Please have standardization as the first step.

2). P(X>12) =

3). P(X>12.8) + P(X<12.8) =

4). P(10.5
4. Suppose X follows a uniform distribution with a=1 and b=9.

1) Mean of X

2) Standard deviation of X

3) What is the probability that the selected values are between 4 and 5 and why? That is, P(4

Answer 1

To calculate the probabilities, standardization or z-score can be used. The range of x values that includes 68.27 percent of the data is 12 to 18.

Step-by-step explanation:

To calculate the probabilities, we need to use standardization, also known as z-score.

1) P(X> 12) = 1 - P(X<= 12) = 1 - P(z<= (12-15)/3) = 1 - P(z<= -1) = 1 - 0.1587 = 0.8413

2) P(X> 12.8) + P(X< 12.8) = P(z>= (12.8-15)/3) + P(z< (12.8-15)/3) = P(z>= -0.4) + P(z<-0.4) = 0.6554 + 0.3446 = 1

3) The range of x values that includes 68.27 percent of the data is the interval that is 1 standard deviation away on both sides of the mean. So, the range of x values is 15-3 to 15+3, which is 12 to 18.