Statistics and Probability Answers

Question No. 4

The Gauteng chamber of business conducted a survey amongst 17 furniture retailers to identify the percentage of bad debts in each company’s debtors’ book. The bad debts percentages are as follows:

2.2, 4.7, 6.3, 5.8, 5.7, 7.2, 2.6, 2.4, 6.1, 6.8, 2.2, 5.7, 3.4, 6.6, 1.8, 4.4, 5.4

Calculate the Pearson Coefficient of skewness coefficient for percentage of bad debts. Is the data skewed?

State the null and the alternative hypothesis in words and in symbols. State whether the test is directional (one-tailed) or non-directional (two-tailed). If it is directional, tell whether if it is left-tailed or right tailed. 

a.) A teacher wants to know if listening to popular music affects the performance of pupils. A class of 50 grade 1 pupils was used in the experiment. The mean score was 82 and the standard deviation is 5. A previous study revealed that µ = 81 and the standard deviation = 10.  

Given the population 5, 10, 15, 20, 25 a) How many samples of size 3, can be drawn with replacement from this population b) Compute and tabulate the sampling distribution of the mean from samples of size 3. c) Verify the results of mean and variance of sampling distribution of the mean. 

Given the population 5, 10, 15, 20, 25

a) How many samples of size 3, can be drawn with replacement from this population

b) Compute and tabulate the sampling distribution of the mean from samples of size 3.

c) Verify the results of the mean and variance of the sampling distribution of the mean. 

If on the average, (r + 1) cars enter a certain parking lot per minute, what is the probability that during any given minute (i): 4 or more cars will enter the lot? (ii): exactly 4 cars will enter? 

It is claimed that the average monthly income of chemical engineers last year was P27,900. A random

sample of 35 chemical engineers is selected and it is found out that the average monthly salary is P28,000.

Using 0.01 level of significance, can it be concluded that there is an increase in the average monthly income

of chemical engineers? Assume that the population standard deviation is P250.50.

A sample of 40 farmers comprises of 25 adopters and 15 non-adopters of organic fertilizer. Also 15 the adopters grow cowpea, while 7 of the non-adopters grow rice. Determine the probability that the first person interviewed was either a non-adopter or someone that grow cowpea

The random variable X, representing the number of defective laptops purchased by an office from a shipment of 20 computers, has the probability distribution function , x ? C C C f ( x ) x r x r     5 20 5 20 a) Assign values to x b) Find its cumulative distribution function and probability of purchasing 3 defective laptop. 

The given table shows the rainfall of Gujarat Region. Forecast the rainfall using

Exponential Smoothing. Use Alpha =0.2, 0.5 and 0.8. Data is available from 1997 to

2016, use this series for the calculation and forecast the rainfall for the year 2017. To

know, what extent the prediction is correct, actual rainfall for 2017 (1024.4millimeters) is provided Based on MSE and MAD, find out which alpha values

among the three suggestions are relatively near to actual value?

SUBDIVISION YEAR ANNUAL (in MM)

Gujarat Region 1997 1068.9

Gujarat Region 1998 1070

Gujarat Region 1999 568.4

Gujarat Region 2000 550.6

Gujarat Region 2001 849

Gujarat Region 2002 637.2

Gujarat Region 2003 1160.3

Gujarat Region 2004 1005.8

Gujarat Region 2005 1316.4

Gujarat Region 2006 1478

Gujarat Region 2007 1178.9

Gujarat Region 2008 911.1

Gujarat Region 2009 641.6

Gujarat Region 2010 1088.7

Gujarat Region 2011 890.5

Gujarat Region 2012 714

Gujarat Region 2013 1118.6

Gujarat Region 2014 705.7

Gujarat Region 2015 622.9

Gujarat Region 2016 764.9

A poll is taken among residents of a city and its suburbs to determine the feasibilities of 

a proposal to construct a civic center. If 6𝒐𝒇 𝟓𝟎 city residents favor the proposal and 

6 𝒐𝒇 𝟕𝟎 suburban residents favor it, find a 𝟗𝟓% confidence interval for the true 

difference between the proportion of city and suburban residents who favor the proposal 

to construct the civic center.