##### Question

In: Computer Science

# Refer to the country in Example 4.11 on p. 91, where household incomes follow Normal distribution...

Refer to the country in Example 4.11 on p. 91, where household incomes follow Normal distribution with µ = 900 coins and σ = 200 coins. (a) A recent economic reform made households with the income below 640 coins qualify for a free bottle of milk at every breakfast. What portion of the population qualifies for a free bottle of milk? (b) Moreover, households with an income within the lowest 5% of the population are entitled to a free sandwich. What income qualifies a household to receive free sandwiches?

## Solutions

##### Expert Solution for normal distribution,
mu = 900
sigma = 200

a)

x = 640
z = (x-mu)/sigma //converting to standard normal distribution
z = (640-900)/200 = -1.3
probability of z<-1.3 = 0.0968

this probability is calculated using Q function (gaussian cdf). This is found using tables or online calculators or definite integration

Probability = 0.0968

Percentage of population = 9.68%

---------------------

b)
lowest 5 percent = 0.05 probability
probability of z = 0.05
z = -1.65 (approx from table using interpolation)
z = (x-mu)/sigma
x = z*sigma+mu = 900-1.65*200 = 570
the income qualified for free sandwich is 570 coins (approx) or less

--------------------------

(checkout -1.3 and -1.65 in this table) ## Related Solutions

##### Question: In country A, the household incomes are normally distributed, with the mean 25000 dollars and...
Question: In country A, the household incomes are normally distributed, with the mean 25000 dollars and the variance 10000^2 dollars. (a) If the poverty level is 10000 dollars, what percentage of the population does not live in poverty? (b) A new tax law is expected to benefit "middle income" households, those with incomes between 20000 dollars and 30000 dollars. What percentage of the population will benefit from the new tax law? (c) What is the probability that the mean size...
##### Many variables in medicine follow a normal distribution where there are approximately an equal number of...
Many variables in medicine follow a normal distribution where there are approximately an equal number of values below the mean as above the mean. Describe two variables that would probably follow a normal distribution. Also note which of the two variables would be likely to have a larger standard deviation and why. As an alternative question, what are some other potential probability distributions in the health care field such as bimodal, skewed, or exponential and give variables that would probably...
##### Name three properties of a normal distribution. Give an original example of a normal distribution in...
Name three properties of a normal distribution. Give an original example of a normal distribution in "real life". Plesae type instead of writing
##### Find an example of application of Normal Distribution (or approximately Normal Distribution) in your workplace or...
Find an example of application of Normal Distribution (or approximately Normal Distribution) in your workplace or business or any example of Normal Distribution. Prove that the variable has the characteristics of a Normal Distribution. Recall that the variable must be continuous and the distribution must be symmetrical (or approximately symmetrical). To prove that the distribution is approximately symmetrical select 20 random observations (measurements/data) of the variable and run a Descriptive Statistics using your calculator or Excel. Just copy the output...
##### Normal Distribution Create an example of each of the three types of normal distribution problems. The...
Normal Distribution Create an example of each of the three types of normal distribution problems. The project will be graded on: (3 points each) Each example of one of the problem types. (1 point) Clear writing style and examples
##### Historically, the one-year returns follow approximately the normal distribution. The one-year return for the S&P 500...
Historically, the one-year returns follow approximately the normal distribution. The one-year return for the S&P 500 was +27% (that is, 0.27) and its standard deviation is 20% (that is, 0.2). What is the probability that a stock in the S&P 500 gained 30% or more last year? (a) 0.0668 (i.e., 6.68%) (b) 0.4404 (i.e., 44.04%) (c) 0.5596 (i.e., 55.96%) (d) 0.9332 (i.e., 93.32%) What is the probability that a stock in the S&P 500 lost 10% or more last year?...
##### The distribution of weights for an industrial part appears to follow a normal distribution. You randomly...
The distribution of weights for an industrial part appears to follow a normal distribution. You randomly selected 21 parts from a large batch of those parts, and determined the sample standard deviation = 4 g. If you want to test H0: σ2 = 16 versus Ha: σ2 ≠ 16, what is the absolute value of the test statistic you would use?
##### Describe in your own words the standard normal distribution. Additionally, give a real-life example of where...
Describe in your own words the standard normal distribution. Additionally, give a real-life example of where we may use the standard normal distribution.
##### The diameters of a batch of ball bearings are known to follow a normal distribution with...
The diameters of a batch of ball bearings are known to follow a normal distribution with a mean 4.0 in and a standard deviation of 0.15 in. If a ball bearing is chosen randomly, find the probability of realizing the following event: (a) a diameter between 3.8 in and 4.3 in, (b) a diameter smaller than 3 9 in, (c) a diameter larger than 4.2 in.