What is the product? (9 t minus 4)(negative 9 t minus 4) negative 81 t squared minus 16 negative 81 t squared + 16 negative 81 t
2 answers:
You might be interested in
Answer:
Yes, he made a reasonable inference by saying about 25 percent of students choose the science.
Step-by-step explanation:
Given that
Number of students for survey = 50
Number of students who choose science = 12
Now
Percentage of student who choose science =
Percentage of student who choose science =
Percentage of student who choose science = 24 %
Now as Mr. Yule said "about 25" percent of students choose the science it can be treated as reasonable approximation.
Now if the number of students in survey become 200, then we can expect 12 out of every 50 students would choose the science. So, in total 48 students would choose the science.
Now lets calculate the percentage of students who choose science.
Percentage of student who choose science =
Percentage of student who choose science =
Percentage of student who choose science = 24 %
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.