Answer:
The lowest 10 percent of the citizens would need at least 52.8 minutes to complete the form.
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 = 40, \sigma = 10[/tex]
The slowest 10 percent of the citizens would need at least how many minutes to complete the form
This is the value of X when Z has a pvalue of 0.9. So it is X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 40}{10}[/tex]
[tex]X - 40 = 1.28*10[/tex]
[tex]X = 52.8[/tex]
The lowest 10 percent of the citizens would need at least 52.8 minutes to complete the form.
