Statistics and Probability Answers

In a certain federal prison, it is known that 2/3 of the inmates are under 25 years of age. It is also known that 3/5 of the inmates are male and that 6/8 of the inmates are female or 25 years of age or older. What is the probability that a prisoner selected at random from this prison is female and at least 25 years old?

Suppose that the average number of hours a household personal computer is used for entertainment is two hours per day. Assume the times spent on entertainment are normally distributed and the standard deviation for the times is half an hour.

(a) Find the probability that a household personal computer is used for entertainment between 1.8 and 2.75 hours per day.

(b) Find the maximum number of hours per day that the bottom quartile of households uses a personal computer for entertainment.

You have a group of individuals randomly split into smaller groups and completing different tasks. For example, you might be studying the effects of tea on weight loss and form three groups: green tea, black tea, and no tea. Perform ANOVA test to find out whether green tea is more effective or black tea for the following data set: (g, 0.1), (g, 0.2), (g, -0.3), (g, 0.0), (g, -0.1), (b, 0.1), (b, 0.1), (b, 0.2), (b, 0.2), (n, 0.0), (n, 0.1), (n, 0.2), (n, -0.05), (n, 0.1) where each pair represents an element of data set comprised of observations of 5 continuous days on 3 different persons having different tea intake. Element's first entity tells whether a person is taking g (green tea), b (black tea) or n (no tea) and second entity tells the change in weight (positive = gain, negative = loss)

With equal probability, the observations 5, 10, 8, 2, and 7 show the number of defective

units found during five inspections in a laboratory. Find (a) the first four central moments,

(b) central moments from the moments about origin and (c) central moments from the

moments about an arbitrary value 8.

A shipment of 8 similar microcomputers to a retail outlet contains 3 defectives. If a school makes a random purchase of 2 of these computers, nd the probability distribution for the number of defectives. also obtain the cumulative probability distribution.

1. The sales of Proton Saga in Kuala Lumpur at AD Sdn Bhd during the past 5 years are as

follows:

YEAR SALES FORECAST

1 450 410

2 495

3 518

4 563

5 584

a) Using the trend projection method, develop a forecast for the sales of Proton Saga in

Kuala Lumpur through year 6.

b) What is the MAD?

The training director of a company is trying to evaluate three different methods of training new employees. The first method assigns each to an experienced employee for individual help in the factory. The second method puts all new employees in a training room separate from the factory, and the third method uses films and programmed learning materials. The training director chooses 18 new employees assigned at random to the three training methods and records their daily production after they complete the programs. Below are productivity measures for individuals trained by each method.

Method 1           Method 2        Method 3

45                   59                41

40                   43                37 

50                   47                43

39                   51                40

53                   39                52

44                   49                37

At 0.05 level of significance, do the three training methods lead to different levels of productivity? Use F tabulated value 3.68. (use ANOVA)

Consider a binomial random variable X with n = 7 and p = 0.3. What is the P(X = 3) *

0.126

1.47.

2.1

0.874

0.227

The body weights (kg) of 20 pregnant mothers attending to an antenatal Clinic were reported as Follows. 55,60,62,65,70,85,60,70,56,63,65,60,60 ,59,72,80,62,70,82,62 

1.Construct the class intervals with 7 classes.

2 Find the cumulative frequency

3 Create frequency distribution table

4 find mean, mode ,median

An Urban council has installed 2000 lamps with mercury bulbs in the   streets of town area. The lifetimes of these bulbs are normally distributed with a mean of 1200 burning hours and having a standard deviation of 200 hours. 

(1) After what number of burning hours would you expect that 10 % of the bulbs would fail?

(2) After what number of burning hours would you expect that 150 bulbs are still in good condition?

I need the answers with simple functions and little explanations.