Asked by Morgan Crouse on Jul 11, 2024
Verified
If the random variable x is normally distributed with a mean equal to .45 and a standard deviation equal to .40, then P(x 
.75) is:
A) .7500
B) .7734
C) .2266
D) .2734
E) .4525
Standard Deviation
An appraisal of the diversity or spread level exhibited by a collection of figures.
Normally Distributed
Refers to a probability distribution which is evenly shaped around the mean, indicating that occurrences of data close to the mean are more common than occurrences of data distant from the mean.
Mean
The average of a set of numbers, calculated by dividing the sum of these numbers by their quantity.
- Identify probabilities and inferential statistics for variables characterized by a normal distribution.
- Interpret and calculate z-scores and their related probabilities.
Verified Answer
JM
Javeria MalickJul 15, 2024
Final Answer :
C
Explanation :
To solve this problem, we need to standardize the random variable x using the formula z = (x - μ) / σ, where μ is the mean and σ is the standard deviation. Thus, z = (.75-.45)/.4 = .75. To find the probability P(x <. 75), we need to find the area to the left of z = .75 on a standard normal distribution table. Looking at the table, we see that the area to the left of z = .75 is .7734. However, we want the area to the right of z = .75, so we subtract .7734 from 1 to get .2266. Therefore, the answer is C.
Learning Objectives
- Identify probabilities and inferential statistics for variables characterized by a normal distribution.
- Interpret and calculate z-scores and their related probabilities.