The tensile strengths of alloy cables produced by industrial extrusion machines are normally distributed. Machine $X$ produces cables with a mean tensile strength of 450 MPa and a standard deviation of 24 MPa.

Find the probability that a cable from Machine $X$ has a tensile strength of less than 414 MPa.

In a production batch of 600 cables from Machine $X$ , determine the expected number of cables having a tensile strength of less than 414 MPa.

Another machine, Machine $Y$ , produces cables with a mean tensile strength of 465 MPa. It is known that $12%12\%$ of these cables have a tensile strength of less than 435.6 MPa.

Calculate the standard deviation of the tensile strengths of cables from Machine $Y$ .

Both machines operate at the same utility cost per cable.

State which machine you would recommend for procurement. Give reasons for your answer.

Find the probability that a cable from Machine $X$ has a tensile strength of less than 414 MPa.

In a production batch of 600 cables from Machine $X$ , determine the expected number of cables having a tensile strength of less than 414 MPa.

Another machine, Machine $Y$ , produces cables with a mean tensile strength of 465 MPa. It is known that $12%12\%$ of these cables have a tensile strength of less than 435.6 MPa.

Calculate the standard deviation of the tensile strengths of cables from Machine $Y$ .

Both machines operate at the same utility cost per cable.

State which machine you would recommend for procurement. Give reasons for your answer.

3.2 Finding Probabilities for Normal Distributions

Question 23

Markscheme

3.2 Finding Probabilities for Normal Distributions

Question 23

Markscheme

3.2 Finding Probabilities for Normal Distributions

Question 23

3.2 Finding Probabilities for Normal Distributions Questions

3.2 Finding Probabilities for Normal Distributions

Question 23

3.2 Finding Probabilities for Normal Distributions Questions