PROBLEM 6E

The torque required to remove bolts in a steel plate is rated as very high, high, average, and low, and these occur about 30%, 40%, 20%, and 10% of the time, respectively. Suppose n = 25 bolts are rated; what is the probability of rating 7 very high, 8 high, 6 average, and 4 low? Assume independence of the 25 trials.

Answer:

Step 1 of 1 :

Given the torque to remove bolts in steel plate is

Very high is 30%,high is 40%,average is 20% and low is 10%.

Then n=25 bolts are rated.

Our goal is to find

What is the probability of rating 7 very high,8 high,6 average and 4 low.

Now we have to find the probability of rating 7 very high,8 high,6 average and 4 low.

Let is the high = 8

Let is the average = 6

Let is the low = 4 and

n is 25 bolts.

Here Very high is 30% = 30/100

Very high is 0.30

High is 40% = 40/100

High is 0.40

Average is 20% = 20/100

Average is 0.20 and

Low is 10% = 10/100

Low is 0.10

Then the probability of rating 7 very high,8 high,6 average and 4 low is

We know that ,,and values.

Then substitute ,,and values.

Here ,and

Then,

Therefore the probability of rating 7 very high,8 high,6 average and 4 low is

0.00405.