I need some help figuring this question out:
Let x be a random variable that represents the speed of the first vehicle passing an observation point between 11am to 12n on a remote highway, automatically recorded by a police radar. Based on past recording over many days, the random variable has an approximate normal distribution with a mean of 72 mph and a standard deviation of 5 mph.

a) What is the probability that, on the next day, the speed of the first vehicle passing the observation point between 11am to 12n is less than 65 mph?

b)What is the probability that, on the next day, the speed of the first vehicle passing the observation point between 11am to 12n is greater than 75mph?

c)What is the probability that, on the next day, the speed of the first vehicle passing the observation point between 11am to 12n is between 65mph and 75mph?

d) On 80% of the days in the coming tear, the sped of the first vehicle passing the observation point between 11am to 12n will be below what value?

e) On each day of the next week from M-F, the sped of the first vehicle passing the observation point between 11am to 12n will be recorded. What is the probability that the average speed of these 5 recordings is more than 70mph?

Solution Summary

The solution provides step by step method for the calculation of probability using the Z score. Formula for the calculation and Interpretations of the results are also included.

A continuous random variable, x, is normally distributed with a mean of $1000 and a standard deviation of $100. Convert each of the following x values into its corresponding z-score.
a. x = $1000
b. x = $750
c. x = $1100
d. x = $950
e. x = $1225
2.Using the standard normal table, find the following probabilities

Consider a population with m(mean)=93.3 and s(standard deviation)=5.27
(A) Calculate the z-score for x =94.9 from a sample of size 12.
(B) Could this z-score be used in calculating probabilities using a standard normal distribution table? Why or why not?

A normal distribution has a mean of u= 40 and o=10. if a vertical line is drawn through the distribution at x= 55, what proportion of the scores on the right side of the line?
A normal distribution has a u= 80 and o= 10. what is the probability of randomly selecting a score greater than 90 from this distribution?
A normal

Standard normal probabilities
Let Z be a standard normal random variable. Calculate the following probabilities using the calculator provided. Round your responses to at least three decimal places.
P (z > - 0.82) =
P (z ≤ 0.77) =
P( -0.81 < z < 1.25) =

1. Given that z is a standard normal random variable, compute the following probabilities.
a. p (z = 2.0)
b. p (z ≥ 1.4)
c. p (-1.0 < z < 0.5)
d. p (1.0 < z < 1.2)
2. The time needed to drive from city A to city B is normally distributed with a mean of 180 minutes and standard deviation of 20 minutes.
a. Wha

At one university, the distance to students' home is normally distributed with a mean of 200 miles and a standard deviation of 25 miles.
a. what is the probability of a student living more than 241.25 miles from the school?
b. what % of students live between 180 and 220 miles from the school?

If the random variable z is the standard normal score, which of the following probabilities could easily be determined without referring to a table?
A. P(z > 2.86)
B. P(z < 0)
C. P(z < - 1.82)
D. P(z> -0/5)

The Modulus of rupture (MOR) for a particular grade of pencil lead is known to be 6500 psi with a standard deviation of 250 psi.
a. Find the probability that a random sample of 16 pencil leads will have an average MOR between 6400 and 6550 psi.
b. What did you assume in order to find this probability?

We are using a chart on standard normal (z) distribution: cumulative area from the LEFT showing Negative x Scores on one side and Positive (z) scores on the other.
a. P(z>2.61).
b. P(-1.62 < z < 2.81).
c. The z-score that would create a right tail of 31%.
d. The z-score that would create a left tail of 6.5%.