Write a coordinate proof given quadrilateral ABCD with vertices A (3, 2), B (8, 2), C (5, 0), and D (0, 0).
1 answer:
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Using the normal distribution, we have that:
- For a single value, P(X < 79.1) = 0.5517.
- For the sample of n = 155, P(X < 79.1) = 0.9463.
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.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
The mean and the standard deviation are given, respectively, by:
.
The probability is the <u>p-value of Z when X = 79.1</u>, hence:
Z = (79.1 - 76.2)/22.4
Z = 0.13
Z = 0.13 has a p-value of 0.5517.
Hence: P(X < 79.1) = 0.5517.
For the sample of 155, applying the Central Limit Theorem, the standard error is:
s = 22.4/sqrt(155) = 1.8
Hence:
Z = (79.1 - 76.2)/1.8
Z = 1.61
Z = 1.61 has a p-value of 0.9463.
P(X < 79.1) = 0.9463.
More can be learned about the normal distribution at brainly.com/question/15181104
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Answer:
Step-by-step explanation:
a)
b) Sample mean is the average of sample
c) std deviation of the sample
d) std dev/sq rt n
e) (sample mean - mu)/std error
f) p value = prob with test statistic
g) If p < alpha, reject H0.
h) If rejected, there is evidence that significant difference between population mean and sample mean.