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If X is binomially distributed with mean 3.20 and variance 1.152, find the complete binomial probability distribution
Suppose that the tires of a certain brand have mean life 25,430 km and standard
deviation 1,800 km.
(a) If a tire is randomly selected, what is the probability that its life is longer than 25,000 km?
(b) Determine the minimal sample size needed so that the probability of the sample mean life longer than 25,000 km is at least 0.97. [15 marks]
In the manufacturing process, a compact disc is acceptable if its diameter is between 120.00mm and 120.20mm. A new machine produces compact discs whose diameters are normally distributed with mean 120.11mm and standard deviation 0.05mm.
(a) What is the probability that a randomly selected compact disc is acceptable?
(b) If four compact discs are randomly selected, what is the probability that at least two of them are not acceptable?
THX!
1. What percentage of the scores in a normal distribution lie below a z-score of 1.65?
a. 1.65% b. 15% c. 45% d. 60% e. 75% f. 90% g. 95%
(a) State the appropriate null and alternative hypothesis. (2)
(b) State and calculate the appropriate test statistic. (8)
(c) Determine the critical value of the test or the pà ¢ value of the test. (4)
(d) State whether or not you reject the null hypothesis, giving the reason. (3)
(e) Draw an appropriate conclusion.
Four groups of 4 patients each were subjected to four different types of treatment for the same ailment. The following data are on the number of days that elapsed before they were completely cured. What conclusions may be drawn about the four types of treatment?
Patient 1: Treatment A is 10, Treatment B is 11, Treatment C is 3. Treatment D is 6
Patient 2: Treatment A is 9, Treatment B is 11, Treatment C is 4. Treatment D is 10
Patient 3: Treatment A is 6, Treatment B is 18, Treatment C is 5. Treatment D is 8
Patient 4: Treatment A is 7, Treatment B is 6, Treatment C is 7. Treatment D is 11
The number of fishing rods selling each day is given below. Perform analyses of the time series to determine which model should be used for forecasting.
a. 3 day moving average analysis
b. 4 day moving average analysis
c. 3 day weighted moving average analysis with weights w1=0.2, w2=0.3 and w3=0.5 with w1 on the oldest data
d. exponential smoothing analysis with a = 0.3.
e. Which model provides a better fit of the data?
f. Forecast day 13 sales of fishing rods using the model chosen in part (e).
Day
Rods sold
1 60
2 70
3 110
4 80
5 70
6 85
7 115
8 105
9 65
10 75
11 95
12 85
in a certain school is known to be normally distributed with a mean of P70 and a standard deviation of P20. A random sample of 16 students will be taken.
What are the two values that are within P10 of the true mean?
Consider that in a population of Filipino adults ages 18 to 65, Body Mass Index (BMI) is normally distributed with a mean of 28 and a standard deviation of 6. What is the BMI mark of the bottom 20% of the distribution of this population? *
#340153 on Dec 2023