Respuesta :
Answer:
Probability = 0.23572 .
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
Since, X ~ N([tex]\mu,\sigma^{2}[/tex])
The z probability is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1) where, [tex]\mu[/tex] = 35 and [tex]\sigma[/tex] = 15
So, P(31 < X < 40) = P(X < 40) - P(X <= 31)
P(X < 40) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{40-35}{15}[/tex] ) = P(Z < 0.33) = 0.62930
P(X <= 31) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{31-35}{15}[/tex] ) = P(Z < -0.27) = 1 - P(Z <= 0.27)
= 1 - 0.60642 = 0.39358
Therefore, P(31 < X < 40) = 0.62930 - 0.39358 = 0.23572 .
