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F(x) = 5x2 -8x + 10
F(x) = x2 + 9x - 4
Heights of the students in a class are given in the distribution below:
5' - 5'2" 11
5'2" - 5'4" 40
5'4" - 5'6" 25 .
Find:
1. Distribution
F(x) = 4x2 + 6x
A random sample of size 15 has 50 as mean, the sum of the
squares of the deviation taken from mean is 130. Can this
sample be regarded as taken from the population having 53 as
mean? Obtain 95% and 99% confidence limits of the mean
for the population.(t test example)
the weight of all male senior high school students from one province is measured and is found to be approximately normally distributed with a mean of 115 lbs and standard deviation of 3 lbs. find the percentile rank of the following weights?
A. 112 lbs
B. 115 lbs
Two years ago, 75% of a financial bank’s customers were satisfied with the service provided by the bank. The bank manager would like to test if the percentage has changed over the time.
a) What hypothesis should be tested?
b) From a survey on 20 random samples, 13 customers are satisfied. Determine the rejection region at .
c) Calculate p-value.
d) If the probability of incorrectly rejecting a true H0 is 0.01, what decision shall you obtain?
A type of treatment has been identified to produce cement compression strength of 5000 kg/cm² with a standard deviation of 120. To test the null hypothesis that = 5000 against the alternative hypothesis that < 5000, a random sample of 50 pieces of cement was tested. The rejection region is defined as x < 4970.
a) Define Type I and Type II Error for the testing.
b) Calculate the probability of Type II Error if = 4960.
c) What is the power of the test?
In the year 1918 a flu like disease occurred in Spain and spread to the rest of the world. This year 2020 another similar flu like disease has occurred in china and is spreading in the whole world. Researchers have found that the likelihood of the disease occurring again is 0.01.Determine the average number of flus in the next 300 years and the likelihood that in the next 300 years, the disease will occur at most five times. (6 marks)
- Verify that (xy2 -1) dx + (x2y) dy is exact and hence solve it.
- Solve: dy/dx - y = e2x , y(0) = 7
- The differential equation of motion of a simple pendulum is given as d2x/dt2 + g/l*x where x is the dependent variable and t is the independent variable. Find the displacement of the pendulum as a function of time t.
- Solve the equation y//+ y/- 2y- x2 = 0
Suppose the mean number of days to germination of a variety of seeds is 34, with a standard deviation of 4.3 days. What is the probability that the mean germination time of a sample of 250 seeds will be within 0.5 days of the population mean?
#340153 on Dec 2023