Respuesta :
Answer:
0.2857 = 28.57% probability that in a year the shares will be selling between $21 and $24
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
The price is approximately normally distributed with a mean of 20 and a standard deviation of 2.
This means that [tex]\mu = 20, \sigma = 2[/tex]
What is the probability that in a year the shares will be selling between $21 and $24
This is the pvalue of Z when X = 24 subtracted by the pvalue of Z when X = 21. So
X = 24:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24 - 20}{2}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 21:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21 - 20}{2}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a pvalue of 0.6915
0.9772 - 0.6915 = 0.2857
0.2857 = 28.57% probability that in a year the shares will be selling between $21 and $24
