Search & Filtering
Suppose a population consists of the ages of 5 students, as follows: 16, 17, 18, 19 and 20. Construct a sampling distribution of the sample mean using random variable of size n=2. Prepare a probability distribution of the sample means.
The weight (in kg) of grade 11 students in section Z follows a normal distribution with a mean 48 and a standard deviation of . Find the probability that students choosen at random has a weight less than 45
Determine Which of these function are bijection from the set of real number to itself
1- f(x)=-3x+4
2- f(x)=-3x2+7
3- f(x)=(x+1)/(x+2)
Use Theorem 4.2.1 to determine which of the following are subspaces of P3. (a) All polynomials a0 + a1x + a2x2 + a3x3 for which a0 = 0. (b) All polynomials a0 + a1x + a2x2 + a3x3 for which a0 + a1 + a2 + a3 = 0. (c) All polynomials of the form a0 + a1x + a2x2 + a3x3 in which a0, a1, a2, and a3 are rational numbers. (d) All polynomials of the form a0 + a1x, where a0 and a1 are real numbers?
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Which of the following are subspaces of F (-infinity,+infinity)? (a) All functions f in F (-infinity,+infinity) for which f(0) = 0. (b) All functions f in F (-infinity,+infinity) for which f(0) = 1. (c) All functions f in F (-infinity,+infinity) for which f(−x) = f(x). (d) All polynomials of degree 2.
Determine weather the each of the following function from set (a,b c, d)to itself injective
1- the function sending the order quadruple (a,b,c,d)to (b,a,c,d)
2- the function sending the order quadruple (a,b,c,d)to (b,b,d,c)
3- The function sending the order quadruple (a,b,c,d) to ( b,d,c,d)
In a shipment of 10 computers, 3 are defective. Three computers are randomly selected and tested. What is the probability that all three are defective if the first and second ones are not replaced after being tested?
Written Assignment unit 7
Complete the following questions utilizing the concepts introduced in this unit.
1. Find the length of an arc in a circle of radius 10 centimetres subtended by the central angle of 50°. Show your work.
2. Graph f(x) = x Sin x on [-4π, 4π] and verbalize how the graph varies from the graphs of f(x) + or - x.
Graph f(x) =Sin x / x on the window [−5π, 5π] and describe freely what the graph shows. You can use www.desmos.com/calculator to obtain the graphs.
3. A 23-ft ladder leans against a building so that the angle between the ground and the ladder is 80°. How high does the ladder reach up the side of the building? Show the steps of your reasoning.
Prove that every continuous function on (a, b) is integrable
The quality of the drinking water must be monitored as often as possible. One variable of concern is
the pH level, which measures the alkalinity or acidity of the water. A pH below 7.0 is acidic while a pH
above 7.0 is alkaline. A pH of 7.0 is neutral. A water-treatment plant is targeting higher than 8.0 pH. Based
on 16 random water samples, the mean and standard deviation were found to be: 𝑋 ̅=7.6 and s = 0.4. Test
the claim using 5%
Step
1 Describe the population parameter of interest
2 Formulate the null and alternative hypothesis
3 Check the assumptions
4 Choose a signifinance level size for α
5 Select the appropriate test statistic
Compute the test statistic using the appropriate formula
6 State the decision rule for rejecting or not the null hypothesis
7 Compare the computed test statistic and the critical value /s
- Given the population 2,4,6 and 8. Suppose samples of size 3 are drawn from this population.
a. Determine the number of possible samples of size n that can be drawn from a given population of size n.
