An item is regularly priced at $35 . Deandre bought it on sale for 55% off the regular price. Whats the price now?
2 answers:
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Answer:
h = 7.47 m
Step-by-step explanation:
According to the question, we have a right triangle formed by the ladder with the wall and the floor.
The length of the ladder is the hypotenuse and the desired height is the opposite. This is due to the fact that "the ladder makes an angle of 21" 27" with the horizontal". Then, the trigonometric ratio to use is sine:
Using the values given:
Multiplying both sides by 14.5:
Then h = 7.47 m
Answer:
P(35.3 < M < 35.4) = 0.0040.
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 random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
Find the probability that a single randomly selected value is between 35.3 and 35.4
This is the pvalue of Z when X = 35.4 subtracted by the pvalue of Z when X = 35.3. So
X = 35.4
By the Central Limit Theorem
has a pvalue of 0.9927
X = 35.3
has a pvalue of 0.9887
0.9927 - 0.9887 = 0.0040
So the answer is:
P(35.3 < M < 35.4) = 0.0040.