Answer:
5040
Step-by-step explanation:
The given series is :
24 + 48 + 72 + 96 +...+ 480
The first term, a= 24
Common difference, d = 24
The last term,
Let there are n terms in the AP.
So,
There are 20 terms in the series. The sum of 20 terms is :
So, the sum of the given arithmetic series is equal to 5040.
Answer:
There is a 95% chance that values will be within ±2 standard deviations of the mean.
Step-by-step explanation:
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.
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this question:
According to the empirical rule, 95% of the measures are within 2 standard deviations of the mean. So the correct statement is:
There is a 95% chance that values will be within ±2 standard deviations of the mean.