Respuesta :
Answer:
52.79% of examinees will complete the exam on time.
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:
There are 35 questions. The psychologist expects that an examinee will spend an average of 1.66 minutes answering each question, with a standard deviation of 0.73 minutes. This means that the mean and the standard deviation for the time to complete the test is [tex]\mu = 35*1.66 = 58.1, \sigma = 35*0.73 = 25.55[/tex].
What proportion of examinees will complete the exam on time?
The time allowed for the exam is 60 minutes. So this proportion is the pvalue of Z when [tex]X = 60[/tex]. So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{60 - 58.1}{25.55}[/tex]
[tex]Z = 0.07[/tex]
[tex]Z = 0.07[/tex] has a pvalue of 0.5279.
This means that 52.79% of examinees will complete the exam on time.
