Answer:
68
Step-by-step explanation:
Pythagorean theorem: a²+b²=c² a²=32² b²=60² c²=hypotenuse²
32²+60²=c²
1024+3600= c²
4624=c²
Now, take the square root of both sides of the equation to find c
=c
68=c
Widget Indutries had stock that sold at 36 5/8 points. The stock rose 7 1/4 points. What is the new price?
1 answer:
The new price of stock of Widget industries is
<u>Solution:</u>
Given that, Widget Industries had stock that sold at points.
The stock rose points.
We have find what is the new price of the stock ?
Now, we know that, new price of the stock will be combination of sold value of the stock and the new rise of points to the stock
Then, new price of the stock = sold price of stock + rise in points
Converting the mixed fractions, we get
Hence, the new price of the stock is
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Answer:
a) The mean is 10 and the variance is 0.0625.
b) 0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.
c) 10.58 minutes.
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.
Normally distributed with a mean of 10 minutes and a standard deviation of 2 minutes.
This means that
Suppose 64 visitors independently view the site.
This means that
a. The expected value and the variance of the mean time of the visitors.
Using the Central Limit Theorem, mean of 10 and variance of (0.25)^2 = 0.0625.
b. The probability that the mean time of the visitors is within 15 seconds of 10 minutes.
15 seconds = 15/60 = 0.25 minutes, so between 9.75 and 10.25 seconds, which is the p-value of Z when X = 10.25 subtracted by the p-value of Z when X = 9.75.
X = 10.25
By the Central Limit Theorem
has a p-value of 0.8413.
X = 9.75
has a p-value of 0.1587.
0.8413 - 0.1587 = 0.6826.
0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.
c. The value exceeded by the mean time of the visitors with probability 0.01.
The 100 - 1 = 99th percentile, which is X when Z has a p-value of 0.99, so X when Z = 2.327.
So 10.58 minutes.