Melanie invests $8800 in a new savings account which earns 4.6% annual interest, compounded daily. What will be the value of her
1 answer:
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Answer:
Step-by-step explanation:
After travelling two hours, the two cruise ships form a triangle. One of the legs of this triangle will be the distance Cruise A travelled, and another will be the distance Cruise B travelled. We can find the distance they travel using:
Cruise A is travelling at 18 miles per hour for 2 hours. Therefore, Cruise A has travelled:
Cruise B is travelling at 15 miles per hour for 2 hours. Therefore, Cruise B has travelled:
Because we are given the angle between these legs, we can use the Law of Cosines to find the third leg. The Law of Cosines is given by:
, where
,
, and
are interchangeable. Let
represent the distance between the two cruises. We have:
(one significant figure).
Answer:
0.4332 = 43.32% probability that the sample mean is between 21 and 22.
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 normal distributions can be solved using the z-score formula.
In a set with mean and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes 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.
According to a report from a business intelligence company, smartphone owners are using an average of 22 apps per month.
This means that
Standard deviation is 4:
This means that
Sample of 36:
This means that
What is the probability that the sample mean is between 21 and 22?
This is the p-value of Z when X = 22 subtracted by the p-value of Z when X = 21.
X = 22
By the Central Limit Theorem
has a p-value of 0.5.
X = 21
has a p-value of 0.0668.
0.5 - 0.0668 = 0.4332
0.4332 = 43.32% probability that the sample mean is between 21 and 22.