Respuesta :
Answer:
a) [tex]X\sim (29,169)[/tex]
b) 0.1987
c) [tex]P_{70}=35.82[/tex]
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 29 minutes
Standard Deviation, σ = 13 minutes
We are given that the distribution of commute time is a bell shaped distribution that is a normal distribution.
a) Distribution of X
Let X represent the commute time for a randomly selected LA worker. Then,
[tex]X\sim (\mu, \sigma^2)\\X\sim(29,(13)^2)\\X\sim (29,169)[/tex]
b) Probability that a randomly selected LA worker has a commute that is longer than 40 minutes
[tex]P( x > 40) = P( z > \displaystyle\frac{40 - 29}{13}) = P(z > 0.8461)[/tex]
[tex]= 1 - P(z \leq 0.8461)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x > 40) = 1 - 0.8013 =0.1987[/tex]
c) 70th percentile for the commute time of LA workers.
We have to find the value of x such that the probability is 0.7
[tex]P( X < x) = P( z < \displaystyle\frac{x - 29}{13})=0.7[/tex]
Calculation the value from standard normal z table, we have,
[tex]\displaystyle\frac{x - 29}{13} = 0.524\\\\x = 35.812\approx 35.82[/tex]
The 70th percentile for the distribution of commute time of LA workers is 35.81 minutes.
