Respuesta :
Answer:
The standard deviation would have to be reduced to 0.1 in the process to meet this target
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 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 mean is 2 liter.
This means that [tex]\mu = 2[/tex]
The company now wants to reduce its defect probability as 0.0455.
This means that:
P(X < 1.8) = 0.0455/2 = 0.02275
P(X < 2.2) = 0.0455/2 = 0.02275
This means that the pvalue of Z when X = 1.8 is 0.02275. This means that when [tex]X = 1.8, Z = -2[/tex]. We use this to find the new standard deviation [tex]\sigma[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2 = \frac{1.8 - 2}{\sigma}[/tex]
[tex]-2\sigma = -0.2[/tex]
[tex]\sigma = \frac{0.2}{2}[/tex]
[tex]\sigma = 0.1[/tex]
The standard deviation would have to be reduced to 0.1 in the process to meet this target
