The compressive strengths of 40 concrete cylinders have an estimated mean of 60.14 MPa and standard deviation of 5.02 MPa. Assuming the strength to be Normally distributed, what is the probability that 10 cylinders will each have strengths between 45 and 75 MPa?

0.9972

Step-by-step explanation:

Let x be a random variable that represents the strength of concrete cylinders.

Given: The compressive strengths of 40 concrete cylinders have an estimated mean of 60.14 MPa and standard deviation of 5.02 MPa.

The probability that 10 cylinders will each have strengths between 45 and 75 MPa :

Hence, The required probability = 0.9972

you need to show us the graph.

step-by-step explanation:

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .