1 point
1 answer:
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Answer:
B) 0.0069
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
Find the probability that their mean rebuild time exceeds 9.1 hours.
This is 1 subtracted by the pvalue of Z when X = 9.1. So
By the Central Limit Theorem
has a pvalue of 0.9931
1 - 0.9931 = 0.0069
So the answer is B.
Answer:
-6 ≤ x < ∞
Step-by-step explanation:
You want the domain of the function y = √(x+6) -7.
<h3>Domain</h3>The domain of a function is the set of x-values for which the function is defined. On a graph, it is the horizontal extent of the graph.
The square root function is undefined for negative arguments, so that limits the domain of the given function:
x+6 ≥ 0
x ≥ -6 . . . . . domain of the given function
__
<em>Additional comment</em>
When the domain is written in interval notation, both the left and right ends of the interval must be specified.
[-6, ∞)
The square bracket identifies -6 as being part of the domain. The parenthesis is used with ∞, because that number has no specific value.
