Question

The comprehensive strength of concrete is normally distributed with u = 2500 psi and o = 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).

Answer 1

Answer :

Given data is :

Sample size n = 5

Mean =

u= 2500

standard deviation = $\sigma=50$

Here we need to find the probability that a random sample of n = 5 specimens will have a sample diameter that falls in the interval from 2499 psi to 2510 psi.

i.e P(2499 < X < 2510)

P(2499 < X < 2510) = P(X < 2510) - P(X < 2499)

= $P(Z < (2510 - 2500) / (50/\sqrt{5}))-P(Z<(2499 - 2500) / (50/\sqrt{5}))$

=

P(Z < 10/(50/2.236)) – P(Z < -1/(50/2.236))

=

=

Using z tabble values,

= 0.6736 - 0.4812

= 0.1925

therefore,

sample diameter = 0.193