In: Statistics and Probability
2) For a normal distribution, what z-score separates the top 10% from the rest of the distribution?
3) The average speed on a certain highway is μ = 58 with a standard deviation of σ = 10. What portion of cars are traveling between 55 and 65 mph?
Could these questions be answered in full details such as equations etc.. please and thank you!
Solution:-
2)For a normal distribution, what z-score separates the top 10% from the rest of the distribution?
-----> That is,
We have to find,the z-score value that seperates lower 90% and top 10%
That is,we have to find z-score value such that,
P(Z > z-score) =10% =0.1
Therefore,
P( Z <=z-score) =1 - P(Z > z-score)
P(Z<= z-score) = 1 - 0.1
P(Z<=z-score)= 0.9 =90%
That is ,we have to find 90 th percentile
by using Excel command, the value of z-score is calculated as,
IT gives value, of z-score as,
z-score =1.281551566
3)The average speed on a certain highway is μ = 58 with a standard deviation of σ = 10. What portion of cars are traveling between 55 and 65 mph?
----> we have
Let X:the speed of cars on certain highway.
μ = 58 and σ = 10
Now, we have to find, proportion of cars are travelling between 55 and 65 mph
That is,
We know result,
Therefore,
Now by using Excel command, this can be calculated as,
It gives value,
The proportion of cars are traveling between 55 and 65 mph =0.1401 =14.01%
Note:-
1) for any continuous distribution,
2) For N (0,1) distribution
i) Excel command for,The (p)th percentile value is given by
ii) Excel command for probability is