Brittany was tracking the increasing temperature in the morning. At 8 a.m., it was 68 degrees Fahrenheit. At 10 a.m., it was 74
degrees Fahrenheit. If Brittany made the function f(x) = 3x + 36, what would the 36 represent?
A. The temperature at midnight
B. The rate the temperature was increasing
C. The length of time she recorded for
D.The total change in degrees
A. The temperature at midnight
B. The rate the temperature was increasing
C. The length of time she recorded for
D.The total change in degrees
1 answer:
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Using the <em>normal distribution and the central limit theorem</em>, we have that:
a) The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.
b) There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.
c) There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.
<h3>Normal Probability Distribution</h3>In a normal distribution with mean and standard deviation
, the z-score of a measure X is given by:
- It measures how many standard deviations the measure is from the mean.
- After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
- By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean
and standard deviation
, as long as
and
.
In this problem:
- 22% of couples meet online, hence p = 0.22.
- A sample of 150 couples is taken, hence n = 150.
Item a:
The mean and the standard error are given by:
The sampling distribution is approximately normal, with mean 0.22 and standard error 0.0338.
Item b:
The probability is <u>one subtracted by the p-value of Z when X = 0.25</u>, hence:
By the Central Limit Theorem:
Z = 0.89
Z = 0.89 has a p-value of 0.8133.
1 - 0.8133 = 0.1867.
There is a 0.1867 = 18.67% probability that in a random sample of 150 couples more than 25% met online.
Item c:
The probability is the <u>p-value of Z when X = 0.2 subtracted by the p-value of Z when X = 0.15</u>, hence:
X = 0.2:
Z = -0.59
Z = -0.59 has a p-value of 0.2776.
X = 0.15:
Z = -2.07
Z = -2.07 has a p-value of 0.0192.
0.2776 - 0.0192 = 0.2584.
There is a 0.2584 = 25.84% probability that in a random sample of 150 couples between 15% and 20% met online.
To learn more about the <em>normal distribution and the central limit theorem</em>, you can check brainly.com/question/24663213