Answer: y-1=6(x+7)
Step-by-step explanation:
The formula for point-slope form is . Since we are given the point and slope, we can directly plug them in.
[distribute by -1]
Now, we know that the point-slope form is y-1=6(x+7).
How many integers between 27 and 53 have a remainder of 4 divided by 6
1 answer:
Answer:
There are 4 integers between 27 and 53 that have a remainder of 4 divided by 6.
Step-by-step explanation:
At first we need to find which integers between 27 and 53 are divisible by 6, which are, respectively:
All integers that have a remainder of 4 divided by 6 are found by summing 4 to each element of A, that is:
There are 4 integers between 27 and 53 that have a remainder of 4 divided by 6.
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Answer:
The probability that the mean life expectancy of the sample is less than X years is the p-value of , in which
is the mean life expectancy,
is the standard deviation and n is the size of the sample.
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.
We have:
Mean , standard deviation
.
Sample of size n:
This means that the z-score is now, by the Central Limit Theorem:
Find the probability that the mean life expectancy will be less than years.
The probability that the mean life expectancy of the sample is less than X years is the p-value of , in which
is the mean life expectancy,
is the standard deviation and n is the size of the sample.