Respuesta :
Answer:
The demand for strawberry pies that is exceeded with a probability of 0.08 is 38.1230 strawberry pies.
Step-by-step explanation:
A normal random variable with mean Mu = 31.8 and standard deviation sd = 4.5, is standardized with the transformation:
Z = (X - Mu) / sd = (X - 31.8) / 4.5
For a probability of 0.08, P (Z > k) = P ([(X - 31.8) / 4.5] > k) = 0.08.
P (Z > 1.4051) = 0.08, thus, k = 1.4051
Now, if k = [(X - 31.8) / 4.5], then X = 4.5k + 31.8 = 4.5 (1.4051) + 31.8 = 38.1230.
The demand for strawberry pies that is exceeded with a probability of 0.08 is 38.1230 strawberry pies.
Answer:
A demand of 38.1225 pies has an 8% probability of being excedeed.
Step-by-step explanation:
Problems of normally distributed samples can be solved using 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.
In this problem, we have that:
[tex]\mu = 31.8, \sigma = 4.5[/tex]
Find the demand that has an 8% probability of being exceeded:
This is the value of X when Z has a pvalue of 0.92. So it is X when Z = 1.405.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.405 = \frac{X - 31.8}{4.5}[/tex]
[tex]X - 31.8 = 1.405*4.5[/tex]
[tex]X = 38.1225[/tex]
A demand of 38.1225 pies has an 8% probability of being excedeed.
