Find the necessary confidence interval for the binomial proportion p. (round your answers to three decimal places.) a 90% confidence interval for p, based on a random sample of n = 400 observations from a binomial population with x = 358 successes.

[0.875;0.925]

Step-by-step explanation:

Hello!

You have a random sample of n= 400 from a binomial population with x= 358 success.

Your variable is distributed X~Bi(n;ρ)

Since the sample is large enough you can apply the Central Limit Teorem and approximate the distribution of the sample proportion to normal

^ρ≈N(ρ;(ρ(1-ρ))/n)

And the standarization is

Z= ^ρ-ρ  ≈N(0;1)

√(ρ(1-ρ)/n)

The formula to estimate the population proportion with a Confidence Interval is

[^ρ ± *√(^ρ(1-^ρ)/n)]

The sample proportion is calculated with the following formula:

^ρ= x/n = 358/400 = 0.895 ≅ 0.90

And the Z-value is ≅ 1.65

[0.90 ± 1.65 * √((0.90*0.10)/400)]

[0.875;0.925]

I hope you have a SUPER day!

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

answer: 94

step-by-step explanation: 79+91+92+94+94 = 450 divided by 5 (since there are 5 number that are being added) = 90