Specifications for an aircraft bolt require that the ultimate tensile strength be at least 18 kN. It is known that 10% of the bolts have strengths less than 18.3 kN and that 5% of the bolts have strengths greater than 19.76 kN. It is also known that the strengths of these bolts are normally distributed.

a. Find the mean and standard deviation of the strengths.

b. What proportion of the bolts meet the strength specification?

Answer:

Step 1 of 2:

(a)

In this question, we are asked to find the mean and standard deviation of the strengths.

Specifications for an aircraft bolt require that the ultimate tensile strength be at least 18.

Given 10% of the bolts have strengths less than 18.3and that 5% of the bolts have strengths greater than 19.76

Strengths of these bolts are normally distributed.

Let represent the strength of these bolts.

we are given,

and

Since is normally distributed, we can write,

Now we will use the formula to calculate the mean and standard deviation, since our probability (area) value is given.

Case 1:

From the table, the closest area to 0.10 is 0.1003, and corresponding is .

……………(1)

Case 2:

From the table, the closest area to 0.95 is 0.9495, and corresponding is .

……………(2)

On solving equation (1) and (2), our mean and standard deviation .

Hence mean and standard deviation .