A warehouse contains ten printing machines, four of which are defective. A company selects five of the machines at random, think
1 answer:
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Answer:
Step-by-step explanation:
Hello!
For me, the first step to any statistics exercise is to determine what is the variable of interest and it's distribution.
In this example the variable is:
X: height of a college student. (cm)
There is no information about the variable distribution. To estimate the population mean you need a variable with at least a normal distribution since the mean is a parameter of it.
The option you have is to apply the Central Limit Theorem.
The central limit theorem states that if you have a population with probability function f(X;μ,δ²) from which a random sample of size n is selected. Then the distribution of the sample mean tends to the normal distribution with mean μ and variance δ²/n when the sample size tends to infinity.
As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.
The sample size in this exercise is n=50 so we can apply the theorem and approximate the distribution of the sample mean to normal:
X[bar]~~N(μ;σ2/n)
Thanks to this approximation you can use an approximation of the standard normal to calculate the confidence interval:
98% CI
1 - α: 0.98
⇒α: 0.02
α/2: 0.01
X[bar] ±
174.5 ±
[172.22; 176.78]
With a confidence level of 98%, you'd expect that the true average height of college students will be contained in the interval [172.22; 176.78].
I hope it helps!
Answer:
a. $60
Step-by-step explanation:
We will use simple interest formula to solve our given problem.
, where
A= Amount after t years.
P= Principal amount.
r= Interest rate in decimal form.
t= Time in years.
Let us find amount of loans repayable after 12 months for taking two amounts of $2000 and $1000.
As $2000 and $1000 are less than 2500, so the rate of loan will be 10%.
12 months = 1 year.
Now let us find amount repayable after 12 months for borrowing $1000.
Adding these amounts we will get total repayable amount after 12 months for borrowing $2000 and $1000 separately.
Now let us find repayable amount after 12 months for taking 1 loan. As $3000 is between $2501 and $7500, so rate of loan will be 8%.
Now let us find difference between both repayable loan amounts.
Therefore, the customer should have saved $60, if he had taken out one loan for $3000 and option a is the correct choice.