Question

How many in a car? A study of rush-hour traffic in San Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose that the number of people per car in the population of all cars that enter at this interchange during rush hours has a mean of μ = 1.7 and a standard deviation of σ = 0.85.

What is the probability that the mean number of people in a random sample of 125 cars that enter at this interchange during rush hours is at least 1.9? (Fill in the blanks)

µ_x-bar = _____________

σ_x-bar = _____________

Shape: ____________________________________________________________

P(x-bar ________)

z-score = ______________________

P(x-bar __________) = ________________________________________

Answer 1

The probability distribution in this case is a poisson distribution case, with:

μ(Mean) = 1.7

σ(Standard Deviation) = 0.85

We need to calculate:

P(x>=1.9)= 1 - P(x=0) - P(x=1) ---- (A)

Probability of a poisson distribution is given by P(x;μ)= (e-μ) (μx) / x

P(x=0)= [e-1.7(1.7)0] /0!

= (0.183*1)/1

=0.183

P(x=1)= [e-1.7(1.7)1] /1!

= (0.183*1.7)/1

=0.311

Using (A), we get:

P(x>=1.9)= 1 - P(x=0) - P(x=1)

= 1 -0.183 -0.311

=0.506

Z score: (x-μ)/σ = (1.9-1.7)/0.85= 0.235

Shape: Skewed towards right skewed