Question

Known: Traffic averages 1825VPH

Standard deviation pf 375VPH

Sample of 20 days

A) Use a t distribution to determine the probability of traffic exceeding 2200 VPH and

B) Use a t distribution to determine the t value for where t <0.02 (2%).

Answer 1

Like in normal distribution we have a z-score , in t-dist we have a t-score where

For P(X > x) = ..........We use '>' since if we are calculating the t-dist probabilities from a table we have been given greater than probabilties.

Therefore P(X < x) =

t-score = with 'n - 1' degrees of freedom

Mean = 1825 and Std Dev = 375 Sample size = 20

t-score = with 19 df

A) Use a t distribution to determine the probability of traffic exceeding 2200 VPH

We need to find P(X > 2200)

t-score =

= 4.472

=

I used excel function ' tdist(x,df,1)' (We are using probability in only 1 direction so '1' tail).

B) Use a t distribution to determine the t value for where t <0.02 (2%)

t-value =

We can use the t-dist table where under the df column we need to look for '19' th row and under the '2.5% and 1%' column.

We do this since there is no column for 2% so we will have to interpolate and calculate the values

Using excel function 'tinv(4%,19)' we can get the answer (4% because the excel generates probabilities x%/2 )