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Answer:
a) 0.3520 = 35.20% probability that a hotel room costs $225 or more per night.
b) 0.1038 = 10.38% probability that a hotel room costs less than $140 per night.
c) 0.4878 = 48.78% probability that a hotel room costs between $200 and $300 per night.
d) $251.
Step-by-step explanation:
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.
In this problem, we have that:
a. What is the probability that a hotel room costs $225 or more per night (to 4 decimals)?
This probability is 1 subtracted by the pvalue of Z when X = 225. So
has a pvalue of 0.6480.
1 - 0.6480 = 0.3520
0.3520 = 35.20% probability that a hotel room costs $225 or more per night.
b. What is the probability that a hotel room costs less than $140 per night (to 4 decimals)?
This probability is the pvalue of Z when X = 140. So
has a pvalue of 0.1038.
0.1038 = 10.38% probability that a hotel room costs less than $140 per night.
c. What is the probability that a hotel room costs between $200 and $300 per night (to 4 decimals)?
This probability is the pvalue of Z when X = 300 subtracted by the pvalue of Z when X = 200. So
X = 300
has a pvalue of 0.9599.
X = 200
has a pvalue of 0.4721.
0.9599 - 0.4721 = 0.4878
0.4878 = 48.78% probability that a hotel room costs between $200 and $300 per night.
d. What is the cost of the 20% most expensive hotel rooms in New York City?
This is X when Z has a pvalue of 1-0.2 = 0.8. So X when Z = 0.84
Rounding to the next dollar.
$251.
The transformation of a function may involve any change. The transformation of the function is Right shift by 90 units.
<h3>How does the transformation of a function happen?</h3>The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units:
y=f(x+c) (same output, but c units earlier)
Right shift by c units:
y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k:
Horizontal stretch by a factor k:
Since the function is transformed from f(x)=x to g(x)=x-90, therefore, the transformation of the function is Right shift by 90 units.
Learn more about Transforming functions:
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Answer:
Type I error: Concluding that mean mileage is less than 32 miles per hour when actually it is greater than or equal to 32 miles per gallon.
Step-by-step explanation:
We are given the following in the question:
Hypothesis:
Mean mileage for the Carter Motor Company's new sedan
We can design the null hypothesis and alternate hypothesis as:
Type I error:
- It is the false positive error.
- It is the error of rejection a true hypothesis.
Type II error:
- It is the false negative error.
- It is the non rejection of a false null hypothesis.
Thus, type I error for the given hypothesis is concluding that mean mileage is less than 32 miles per hour when actually it is greater than or equal to 32 miles per gallon.
Type II error would be concluding that mean mileage is greater than or equal to 32 miles per gallon when actually it is less than 32 miles per gallon.