The comprehensive strength of concrete is normally distributed with μ = 2500 psi and σ = 50 psi. Find the probability that a random sample of n = 5 specimens will have a sample mean diameter that falls in the interval from 2499 psi to 2510 psi. Express the final answer to three decimal places (e. g. 0.987).

The probability that a random sample of n = 5 specimens will have a sample values that falls in the interval from 2499 psi to 2510 psi = P(2499 < x < 2510) = 0.192

Step-by-step explanation:

For the population,

μ = 2500 psi and σ = 50 psi

But for a sample of n = 5

μₓ = μ = 2500 psi

σₓ = σ/√n = (50/√5)

σₓ = 22.36 psi

So, probability that the value for the sample falls between 2499 psi to 2510 psi

P(2499 < x < 2510)

We normalize/standardize these values firstly,

The standardized score for any value is the value minus the mean then divided by the standard deviation.

For 2499 psi

z = (x - μ)/σ = (2499 - 2500)/22.36 = - 0.045

For 2510 psi

z = (x - μ)/σ = (2510 - 2500)/22.36 = 0.45

To determine the probability the value for the sample falls between 2499 psi to 2510 psi

P(2499 < x < 2510) = P(-0.045 < z < 0.45)

We'll use data from the normal probability table for these probabilities

P(2499 < x < 2510) = P(-0.045 < z < 0.45) = P(z < 0.45) - P(z < -0.045) = 0.674 - 0.482 = 0.192

use formula for the circle a=3.14

step-by-step explanation:

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2