Respuesta :
Answer:
38.40% probability that it would take between 2.5 and 3.5 hours to construct a soapbox derby car.
Step-by-step explanation:
Problems of normally distributed samples are 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 = 3, \sigma = 1[/tex]
Find the probability that it would take between 2.5 and 3.5 hours to construct a soapbox derby car.
This is the pvalue of Z when X = 3.5 subtracted by the pvalue of Z when X = 2.5
X = 3.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{3.5 - 3}{1}[/tex]
[tex]Z = 0.5[/tex]
[tex]Z = 0.5[/tex] has a pvalue of 0.6915
X = 2.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{2.5 - 3}{1}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a pvalue of 0.3075
0.6915 - 0.3075 = 0.3840
38.40% probability that it would take between 2.5 and 3.5 hours to construct a soapbox derby car.
