Using the normal distribution, it is found that 63.18% of the area under the curve of the standard normal distribution is between z = − 0.9 z = - 0.9.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean 
and standard deviation 
is given by:
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
The area within 0.9 standard deviations of the mean is the <u>p-value of Z = 0.9(0.8159) subtracted by the p-value of Z = -0.9(0.1841)</u>, hence:
0.8159 - 0.1841 = 0.6318 = 63.18%.
More can be learned about the normal distribution at brainly.com/question/4079902
#SPJ1
Is this 2 different questions?
Answer:
2(x + 2)² - 5
Step-by-step explanation:
Given
2x² + 8x + 3
To obtain the required form use the method of completing the square.
The coefficient of the x² term must be 1, thus factor 2 out of 2x² + 8x
= 2(x² + 4x) + 3
add/subtract ( half the coefficient of the x- term)² to x² + 4x
= 2(x² + 2(2)x + 4 - 4) + 3
= 2(x + 2)² - 8 + 3
= 2(x + 2)² - 5
with p = 2 and q = - 5
The answer x = 11 is correct for problem 4. Nice work.
Use this x value to find the answer in problem 5. From problem 4, we're told that Romeo runs at a speed of 5 m/s. If he runs for x = 11 seconds,then he runs a total distance of:
5*x =(5 m/s)*(x meters) = (5 m/s)*(11 seconds) = 5*11 = 55 meters
The answer to problem five is 55 meters
Let x represent amount invested in the higher-yielding account.
We have been given that a man puts twice as much in the lower-yielding account because it is less risky. So amount invested in the lower-yielding account would be 
.
We are also told that his annual interest is $6600 dollars. We know that annual interest for one year will be principal amount times interest rate.
, where,
I = Amount of interest,
P = Principal amount,
r = Annual interest rate in decimal form,
t = Time in years.
We are told that interest rates are 6% and 10%.
Amount of interest earned from lower-yielding account: 
.
Amount of interest earned from higher-yielding account: 
.
Let us solve for x.
Therefore, the man invested $30,000 at 10%.
Amount invested in the lower-yielding account would be 
.
Therefore, the man invested $60,000 at 6%.
