Meg loves to read. Her favorite author is Dr. Seuss. For every 11 books Meg owns 8 are Dr. Seuss books. If Meg has 40 Dr. Seuss
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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:
Step-by-step explanation:
I'll draw a quick sketch. It's hard to "see" this kinda of problem w/o a drawing , so start there. just draw as much as you can from what the problem tells you.
diameter = 14 cm
radius = 7 cm
pi = 3.142
PRQ = 35 °
to find Y use law of sines
sin(70) / Y = sin(55) / 7
sin(70) / sin(55) / 7 = Y ( I'll use my calculator for all the non standard angles )
sin(70) * 7 / sin(55) = Y ( and invert and multiply the fraction in the denom )
8.03007 = Y
x = 70 °
if you have questions, and you should, just put them in the comments , I'll see them later :)
