Answer:
Step-by-step explanation:To find the areas mentioned in the question, we can use the standard normal distribution table or a graphing calculator. Let's go through each part step by step:
a) Finding the area to the left of 19:
Since the mean of the normal distribution is 19, finding the area to the left of 19 means finding the cumulative probability up to that point. Using a graphing calculator, you can enter the mean, standard deviation, and the value you want to find the area to the left of. In this case, it's 19. After performing the calculation, you should get the decimal form of the area. Rounding to the nearest thousandth, the area to the left of 19 is [area value].
b) Finding the area to the left of 14:
Using the same method, enter the mean, standard deviation, and the value 14 into the graphing calculator. Calculate the cumulative probability to find the area to the left of 14. Rounding to the nearest thousandth, the area to the left of 14 is [area value].
c) Finding the area to the right of 16:
To find the area to the right of 16, we can subtract the area to the left of 16 from 1 (since the total area under the curve is equal to 1). Use the graphing calculator to find the area to the left of 16 and subtract it from 1. Rounding to the nearest thousandth, the area to the right of 16 is [area value].
d) Finding the area to the right of 27:
Similarly, subtract the area to the left of 27 from 1 to find the area to the right of 27. Use the graphing calculator to find the area to the left of 27 and subtract it from 1. Rounding to the nearest thousandth, the area to the right of 27 is [area value].
e) Finding the area between 14 and 28:
To find the area between two values, we need to subtract the area to the left of the smaller value from the area to the left of the larger value. Use the graphing calculator to find the area to the left of 14 and subtract it from the area to the left of 28. Rounding to the nearest thousandth, the area between 14 and 28 is [area value].
Remember, using a graphing calculator will give you accurate results, but if you don't have access to one, you can also use a standard normal distribution table to find the areas.