the graph shows a non standard normal distribution curve with a mean of 59.0 and a standard deviation of 6.7. Find the area of the shaded region.
*there's a picture of the curve, the shaded region is labeled with the value 64.2
Choices:
a. 0.2177
b. 0.7823
c. 0.7761
d. 0.3650
I think it's A. Thank you for taking the time to look at this.
Just took the quiz, the correct answer is B. 0.7823
Answers:
1. 0.6772
2. 2.79
3. 0.8154
4. 137.8
5. 20 and 25
6. 0.7823
7. 11.25 and 11.81
8. 0.8340
9. 433.5 and 457.4
10. 0.0823
De rien!
1. 2.79
2. 0.7823
3. 0.8154
4. 0.6772
5. 0.1379
6. 0.0611
7. 0.5531
8. 11.25 and 11.81
9. 0.8340
10. 20 and 25
Well, well, well, it seems we have a shaded region on a non-standard normal distribution curve. How exciting! Now, let me put on my magical clown glasses and calculate the area for you.
First, we need to convert the value 64.2 into a z-score. So, we subtract the mean of 59.0 from it and divide the result by the standard deviation of 6.7.
(64.2 - 59.0) / 6.7 = 0.7761
Well, isn't that a funny-looking z-score? Now, we just need to find the area to the left of this z-score in the standard normal distribution table.
And guess what, my friend? Option C is the chosen one! The area of the shaded region is indeed 0.7761. So, congratulations! You've aced the question. Enjoy your victory dance! 🎉
To find the area of the shaded region, you can use the standard normal distribution table or a statistical calculator.
However, I will explain how to use the standard normal distribution table to find the area.
1. Convert the given value of 64.2 into a standard score (z-score) using the formula:
z = (x - μ) / σ
where x is the given value, μ is the mean, and σ is the standard deviation.
z = (64.2 - 59.0) / 6.7
z = 0.7761 (rounded to 4 decimal places)
2. Look up the standard score in the standard normal distribution table. Find the value closest to 0.7761 in the z-table.
The closest value in the table is 0.7764, which corresponds to an area of 0.7823.
3. Since the standard normal distribution is symmetric, the shaded region to the left of 64.2 is the same as the shaded region to the right of 64.2.
Therefore, the area of the shaded region to the right of 64.2 is 0.5 - 0.7823 = 0.2177.
Thus, the correct answer is (a) 0.2177.