Respuesta :
solution:
we have, mean =8.4 hrs, std. deviation = 1.8 hrs, sample size n = 40 , X = 8.9
Probability(X<8.9) = ?
we know that, Z = (X - mean)/(std. deviation/(sqrt. n)) = (8.9 - 8.4)/(1.8/(sqrt.40))
Z = 1.7568
from standard normal probabilities table, we have , P(Z<1.7568) = 0.9608
Hence, probability that the mean rebuild time is less than 8.9 hours is 0.9608
The probability that their mean rebuild time is less than 8.9 hours is [tex]\boxed{{\text{probability}} = {\text{0}}{\text{.9608}}}[/tex] or [tex]\boxed{{\text{probability}} = 96.08\% }[/tex].
Further Explanation:
The Z score of the standard normal distribution can be obtained as,
[tex]\boxed{{\text{Z}} = \frac{{X - \mu }}{{\frac{\sigma }{{\sqrt n }}}}}[/tex]
Given:
The mean of time is [tex]\boxed{\mu = 8.4{\text{ hours}}}[/tex]
The standard deviation of the time is [tex]\boxed{1.8 hours}[/tex].
The number of mechanics is [tex]\boxed{n = 40}[/tex].
Explanation:
The probability that their mean rebuild time is less than 8.9 can be expressed as [tex]P\left({X < 8.9}\right)[/tex].
The value of standard normal Z can be obtained as follows.
[tex]\begin{aligned}Z&=\frac{{X - \mu }}{{\frac{\sigma }{{\sqrt n}}}}\\&=\frac{{8.9 - 8.4}}{{\frac{{1.8}}{{\sqrt{40}}}}}\\&=\frac{{3.16}}{{1.8}}\\&=1.76\\\end{aligned}[/tex]
The probability of [tex]P\left({X < 8.9}\right)[/tex] is equal to [tex]P\left({Z < 1.76}\right)[/tex].
The value of [tex]P\left({Z < 1.76}\right)[/tex] from the standard normal table is 0.9608.
Hence, the probability that their mean rebuild time is less than 8.9 hours is [tex]\boxed{{\text{probability}} = {\text{0}}{\text{.9608}}}[/tex] or [tex]\boxed{{\text{probability}} = 96.08\% }[/tex].
Learn more:
1. Learn more about normal distribution https://brainly.com/question/12698949
2. Learn more about standard normal distribution https://brainly.com/question/13006989
Answer details:
Grade: College
Subject: Statistics
Chapter: Normal distribution
Keywords: Z-score, Z-value, standard normal distribution, standard deviation, test, measure, probability, low score, mean, normal distribution, percentile, percentage, undesirable behavior, proportion, mechanic, Chevrolet Colorado, rebuild, transmission, study.
