HOW CAN ARITHMETIC AND GEOMETRIC SEQUENCES BECOME LINEAR AND EXPONENTIAL FUNCTIONS?

1 answer:

3 0

The formula of an arithmetic sequence is the following :
$u_n=r\times n+u_0\text{ wherein r is the rate of the sequence}
\\\text{and u0 the first value}\\\text{The above formula is linear wherever }u_0=0.$
A geometric sequence is in the form:
$u_n=u_0r^n\text{, again u0 the first value and r the rate. }\\\text{If }u_0=1\text{ the formula becomes:}\\u_n=r^n=e^{n\log r}\text{ which is an exponential formula.}$

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If the distribution is really (5.43,0.54)

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Answer:

0.7486 = 74.86% observations would be less than 5.79

Step-by-step explanation:

I suppose there was a small typing mistake, so i am going to use the distribution as N (5.43,0.54)

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 pvalue, we get the probability that the value of the measure is greater than X.

The general format of the normal distribution is:

N(mean, standard deviation)

Which means that:

$\mu = 5.43, \sigma = 0.54$