Statistics and Probability Answers

After reviewing previous loan records, the credit manager of a bank determines that the data follows a normal distribution. The debts have a mean of $20 000 and the probability that the loss could be greater than $25 000 or less than $15 000 is 0.418. Determine the standard deviation of the data to the nearest hundred dollars.


A company packages rice into 10 kg bags. The machine that fills the bags can be calibrated to fill to any specified mean with a standard deviation of 0.09 kg. Any bags that weigh less than 10 kg cannot be sold and must be refilled. To what mean value, to the nearest hundredth of a kilogram, should the machine be set if the company does not want to refill more than 1.5% of the bags?

Create a flow chart explaining the procedures (NOT SPSS STEPS!) of one-way ANOVA and post-hoc tests for all types of data (continuous data, ratio, proportion, …). Please include all possible conditions at each level (normally and non-normally distributed data, and homoscedastic and heteroscedastic variance). Assume n = 120.

Data from a random sample of 220 house sales.
Let Price denotes selling price in $1000, BDR denotes the number of bedrooms, Bath
denotes the number of bathrooms, Hsize denotes the size of house in square feet, Lsize
denotes the lot size in square feet, Age denotes the age of the house in years and Poor
denotes a binary variable that is equal to 1 if the condition of the house is reported
as “poor”. Standard errors in parenthesis.

119.2 + 0.485BDR + 23.4Bath + 0.156Hsize + 0.002Lsize + 0.090Age − 48.8Poor,
(23.9) (2.61) (8.94) (0.011) (0.00048) (0.311) (10.5)

1.The p-value is equal to 0.853 for testing the null hypothesis that the coefficient on
BDR is zero. Is that coefficient significantly different from zero at the 5% level?
2. Typically five-bedroom houses sell for much more than two-bedroom houses. Is
this consistent with answer (c)?
3. Lot size (Lsize) is measured in square feet. Is another scale might
be more appropriate?

A bottling machine can be regulated so that it discharges an average of  ounces
per bottle. It has been observed that the amount of ll dispensed by the machine is
normally distributed with  = 1:0 ounce. A sample of n = 9, lled bottles is randomly
selected from the output of the machine on a given day (all bottled with the same
machine setting), and the ounces of lled bottles are measured. Find the probability
that the sample mean will be within 0:3 ounce of the true mean  for the chosen
machine setting.

Suppose that the number of people entering a department store on a given day is a
random variable with mean 50. Suppose further that the amounts of money spent by
these customers are independent random variables having a common mean of GHS
12.00. Finally, suppose also that the amount of money spent by a customer is also
independent of the total number of customers who enter the store. What is the expected
amount of money spent in the store on a given day?

A4. Using the Chebyshev's inequality, nd the value of k that will guarantee that the
probability is 0:95 when the deviation of X from its mean is not more than k.

In the Ministry of Roads and Highways, contracts for two constructions jobs are
randomly assigned to one or more of three rms namely, A;B and C. Suppose that X
is the number of contracts assigned to rm A and Y is the number of contracts assigned
to rm B. It is assume that each rm can receive 0; 1; or 2 contracts. Compute the
expected value of XY , i.e. E(XY ).

Recent studies have shown that 30% of employees in the insurance industry telecommute four days a week. If a random sample of 15 insurance industry employees is taken, what is the probability that
(a) Less than 6 telecommute four days a week?
(b) At least 9 telecommute four days a week?

Z~N (0,1^2) find a) P (Z>2.0) b) P (Z <-2.0) c) P ( -1 <Z <0.5)

The door frames used by abuilder of one standard height 1.830 m the hights of men are normally distributed with mean 1.730 m ansfadard deviation 0.064 m. a) find the proportion of men that will be taller the door frame .b) find the frame height such that one man in a thousand will be taller then the frame height.