) Is it reasonable to compute a 95% confidence interval for π using the normal approximation in this case? If it is possible, explain why, and make the interval. If it is not reasonable, explain why

Full Question:.

Most penguin species are not sexually dimorphic, which means they lack obvious outward body characteristics which indicate sex. Observation of behavior or a blood test can determine Penguin sex. A penguin researcher is interested in estimating the proportion of females in a large penguin population. She takes a random sample of n = 20 penguins and determines the sex of each one using a blood test. She finds 12 males and 8 females. Let π be the proportion of females in the population.

(a) Find a point estimate of π.

(b) Find the estimated standard deviation of your estimate.

(c) Is it reasonable to compute a 95% confidence interval for π using the normal approximation in this case? If it is possible, explain why, and make the interval. If it is not reasonable, explain why.

a. The female penguins are 0.4 in proportion to the male.

b. Standard Error = 0.110

c. Yes, it is.

See Explanation

Step-by-step explanation:

Given

n = 20 penguins

m = Male = 12

f = Female = 8

π = the proportion of females in the population...

a. Calculating a point estimate of π.

This is calculated by dividing number of females by total penguins

π = f/n

π = 8/20

π = 0.4

So, the female penguins are 0.4 in proportion to the male.

b. Calculating Standard Error

Standard Error is calculated by √(pq/n)

Where p = 0.4 --- calculated above

q = 1 - p = 1 - 0.4

q = 0.6

n = 20

Standard Error = √(0.4*0.6/20).

Standard Error = 0.109544511501033

Standard Error = 0.110 -; Approximated

c. Checking Possibilities

Expected Value of Male = 20(0.6) = 12

Expected Value of Female = 20(0.4) = 8

20(0.4) and 20(0.6) are both greater than 5, so we can approximate the distribution as normal. The C sill be (0.18, 0.62).

135 is your answer

step-by-step explanation:

try 180 times three then divide that number by 4 (sides) to get your answer. im glad to : )

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.