Math Answers

Student Expenditures The average expenditure per student (based on average daily attendance) for a certain school year was $10,337 with a population standard deviation of $1560. A survey for the next school year of 150 randomly selected students resulted in a sample mean of $10,798. Do these results indicate that the average expenditure has changed? Choose your own level of significance.

Suppose speeds of vehicles on a particular stretch of roadway are normally distributed with mean 36.6 mph and standard deviation 1.7 mph. Find the probability that the mean speed of 20 randomly selected vehicles is between 35 and 40 mph

A jar contains 8 green, 4 blue, 10 red and 2 yellow skittles A skittle is randomly drawn Replaced then another is drawn Find each probability blue

The gain of an amplifier is found to be 𝐺 = 20 ln(𝑉𝑜𝑢𝑡). The tasks are to find equations for: a) Draw a graph of Gain against Vout between 𝑉𝑜𝑢𝑡 = 1 and 𝑉𝑜𝑢𝑡 = 10 b) Determine the gradient of the graph at 𝑉𝑜𝑢𝑡 = 2 and 𝑉𝑜𝑢𝑡 = 5 c) Find the derivative 𝑑𝐺/ 𝑑𝑉𝑂𝑢𝑡 and calculate its value at 𝑉𝑜𝑢𝑡 = 2 and 𝑉𝑜𝑢𝑡 = 5 d) Compare your answers for part b) and part c) e) Find the second derivative 𝑑²𝐺/ 𝑑𝑉𝑂𝑢𝑡 ² 

The mean score of a group of 24 students in an educational achievement test in reading was 45 with a standard deviation of 6. At the end of the school year, the mean score on an equivalent form of the same test was 50 with a standard deviation of 5. Has the class made significant progress in reading during the year? Use alpha equal to 0.05.

Find a complete integral of x(1 + y)p = y(1 + x)q

A statistics Department had purchased 24calculators in which 4 are defective. Calculators are selected one-after-another without replacement and tested. What is the probability that the second calculator found to be defective is the eighth calculator selected.

(p^q)v(P ^ Q ^ R)

If a string of length l is initially at rest in equilibrium position and each of its points is given the velocity dy/dt= b sin^3πx/l find the displacement

The time between arrivals of 52 patients at an intensive care unit were recorded to the nearest hour. The data are shown below. (20 Marks)

Time (Hours)

[0-20)

[20-40)

[40-60)

[60-80)

[80-100)

[100-120)

[120-140)

Frequency

16

13

7

4

3

4

5

I. Construct a histogram and cumulative frequency polygon for these data.

II. Estimate the percentage of the time between arrivals of patients with less than 80 hours.