Respuesta :
Answer:
0.0668 = 6.68% probability that the average price change of this sample is less than 1.0.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
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 estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean µ = 1.1 and variance σ2 = 0.16. You collect a sample of 36 such price changes.
So the standard deviation is:
[tex]\sigma = \sqrt{\sigma^2} = \sqrt{0.16} = 0.4[/tex]
Sample of 36:
This means that [tex]s = \frac{0.4}{\sqrt{36}} = 0.0667[/tex]
Probability that the average price change of this sample is less than 1.0.
This is the pvalue of Z when X = 1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1 - 1.1}{0.0667}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
0.0668 = 6.68% probability that the average price change of this sample is less than 1.0.
