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2. An electrical company claims that the average life of the bulbs it manufactures is 1 200 hours with a standard deviation of 250 hours. If a random sample of 100 bulbs is chosen, what is the probability that the sample mean will be less than 1150 hours? (5 points)
a. Z = - 2
b. Z = - 3
c. Z = - 4
d. Z = - 5
A person walks 750m due north, then 250m due east. If the entire walk
takes 13 minutes, find the person's average velocity?
An object moves along a straight line. First it travels at a velocity of
12m/s for 6s and then continues at the same direction with 20m/s for 3s.
What is its average speed?
For 10s, the velocity of a car which travels with a constant acceleration,
changes from 10m/s to 20m/s. How far does the car travel?
A cyclist covers a distance of 15 miles in 2 hours. Calculate his speed.
A boy walks at a speed of 4 kmph. How much time does he take to walk a
distance of 20 km?
A car takes 4 hours to cover a distance, if it travels at a speed of 40 mph. What should be its speed to cover the same distance in 1.5 hours?
If a person drives his car in the speed 50 miles per hour, how far can he
cover in 90 minutes?
A person walks 100m in 5 minutes, then 200m in 9 minutes and finally 50
in 4 minutes. Find its average speed?
What is the speed of a rocket that travels 800m in 13s?
A population consists of values (1, 4, 7). Consider all possible samples of size n= 3 that can be drawn without replacement from this population.
a. Find the mean of the population.
b. Find the standard deviation of the population.
c. Find the mean of the sampling distribution of means.
d. Find the standard deviation of the sample distribution of means,
e.Construct the probability histogram of x with replacement
For what values of π does the curve π(π₯) = 2π₯3 + ππ₯2 + 2π₯ have maximum and minimum
points?
Show that the minimum and maximum points of every curve in the family of polynomialsΒ
π(π₯) = 2π₯3 + ππ₯2 + 2π₯ lie on the curve π¦ = π₯ β π₯3.Β
Verify that π¦1(π₯) = 1 and π¦2(π₯) = π₯^(1/2) are solutions of the differential equationΒ π¦π¦β²β² + (π¦β²)^2 = 0 for π₯ > 0. Then show that π¦ = π1 + π2π₯^(1/2) is not, in general, aΒ solution to the equation. Explain why this does not contradict superposition principle.
Random sample of n=2 are drawn from a finite population consisting of the numbers 5,6,7,8,and 9
A.Find the mean population
B.find the standard deviation of the population
C. Find the mean of the sampling distribution of the sample means.
D.FIND The standard deviation of the sampling distribution of the sample means
E.Verify the central limit theorem
A coordinator of a degree program in a university assessed a probability distribution for the number of students (x) entering into the program as follows:
X 30 45 60 65 90 100
f(x) 0.10 0.20 0.20 0.30 0.10 0.10
(i) Is the probability distribution valid? Explain
(ii) What is the probability of 60 or fewer students entering into the program?Β Β
