13. A set of final exam scores in an organic chemistry course was found to be normally distributed, with a mean of 73 and a standard deviation of 8. What is the probability of getting a score higher that 71 on this exam?
73-71 = 2
2/8 = .24 sigma below mean
go to normal distribution table
.5948 of distribution is below .24 sigma above mean
Z =Variable - Mean/ Standard deviation
Z =71-73/8
Z =-2/8
Z = -0.25
Z value -.25 = .401294
To find higher than 71
1 - .401294 = 0.5987
59.87 % will get a score higher than 71 on this exam.
To calculate the probability of getting a score higher than 71 on the exam, we need to standardize the score using the z-score formula and then find the corresponding area under the standard normal curve.
The z-score formula is given by: z = (x - μ) / σ
Where:
x = the value we want to find the probability for (71 in this case)
μ = the mean of the distribution (73 in this case)
σ = the standard deviation of the distribution (8 in this case)
Now we can calculate the z-score:
z = (71 - 73) / 8
z = -0.25
To find the probability of getting a score higher than 71, we need to find the area under the standard normal curve to the right of the z-score (-0.25).
Using a standard normal distribution table or a calculator, we can find that the area to the right of -0.25 is approximately 0.5987.
So, the probability of getting a score higher than 71 on this exam is approximately 0.5987 or 59.87%.
To find the probability of getting a score higher than 71 on the exam, we need to compute the area under the normal distribution curve to the right of 71.
1. Standardize the value 71 using the z-score formula:
z = (x - mean) / standard deviation
Here, x = 71, mean = 73, and standard deviation = 8.
z = (71 - 73) / 8 = -2/8 = -0.25
2. Look up the z-score in the standard normal distribution table (also known as the z-table) to find the corresponding cumulative probability.
3. The z-table provides the probability of obtaining a value less than the given z-score. Since we are interested in the probability of obtaining a value greater than 71, we subtract the cumulative probability (from step 2) from 1 to get the desired probability.
Alternatively, you can use statistical software or an online calculator to find the probability directly by specifying the mean, standard deviation, and cutoff value.
By following these steps, you will find that the probability of getting a score higher than 71 on the exam is approximately 0.5987.