Question

The mean annual inflation rate in the United States over the past 98 years is 3.37% and has a standard deviation of approximately 5%. In 2018, the inflation rate was below 1.9%. If the annual inflation rate is normally distributed, what is the probability that inflation rate will be below 1.9% in 2019?

Answer 1

Answer:

38.59% probability that inflation rate will be below 1.9% in 2019

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

$\mu = 3.37, \sigma = 5$

If the annual inflation rate is normally distributed, what is the probability that inflation rate will be below 1.9% in 2019?

This is the pvalue of Z when X = 1.9. So

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

$Z = \frac{1.9 - 3.37}{5}$

$Z = -0.29$

$Z = -0.29$ has a pvalue of 0.3859

38.59% probability that inflation rate will be below 1.9% in 2019