Respuesta :
Answer:
The probability that it will take less than 6 minutes to complete the test is 0.0266.
Step-by-step explanation:
We are given that the length of time needed to complete a certain test is normally distributed with mean 35 minutes and standard deviation 15 minutes.
Let X = length of time needed to complete a certain test
SO, X ~ N([tex]\mu = 35,\sigma^{2} = 15^{2}[/tex])
The z-score probability distribution is given by ;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean time to complete the test = 35 minutes
[tex]\sigma[/tex] = standard deviation = 15 minutes
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
Now, the probability that it will take less than 6 minutes to complete the test is given by = P(X < 6 minutes)
P(X < 6) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{6 - 35}{15}[/tex] ) = P(Z < -1.933) = 1 - P(Z [tex]\leq[/tex] 1.933)
= 1 - 0.9734 = 0.0266
The above probability is calculated using z table by looking at value of x = 1.933 which will lie between x = 1.93 and x = 1.94 in the z table which have an area of 0.9734.
Therefore, probability that it will take less than 6 minutes to complete the test is 0.0266.
