Statistics

An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are independently and normally distributed with a mean of 120 cm and a standard deviation of 4.7 cm.

Find the probability that if 3 are randomly selected, all 3 have lengths that exceed 122 cm.

1. 👍 0
2. 👎 0
3. 👁 3,269
1. Use z-score formula:

z = (x - mean)/sd

z = (122 - 120)/4.7 = ?

Once you have the z-score, check a z-table for the probability (keep in mind that you are looking for the probability exceeding 122 cm).

After you have the probability from the table, use a normal approximation to the binomial distribution.

Formulas:
mean = np = 3 * p
sd = √npq = √(3 * p * q)
Note: p = probability from z-table; q = 1 - p

Use z-scores again; this time use 3 for x, the mean calculated above, and the standard deviation calculated above.

Once you have this z-score, determine the probability using a z-table once again.

I hope this will help get you started.

1. 👍 1
2. 👎 0

Similar Questions

1. algebra

During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the machine recommends that the temperature of the machine part remain below 141°F. The temperature T in

2. math

A machine has four components, A, B, C, and D, set up in such a manner that all four parts must work for the machine to work properly. Assume the probability of one part working does not depend on the functionality of any of the

3. Statistics

A machine fills 12 ounce bottles with soda. For the machine to function properly, the standard deviation of the sample must be less than or equal to 0.02 ounce. A sample of 8 bottles is selected, and the number of ounces of soda

4. Math

The manager of a manufacturing company knows that they will need a new machine in one of their factories. The new machine will cost them \$13,700. The manager has determined that they can afford to pay 10% of the cost of the

1. statistic

The variance in a production process is an important measure of the quality of the process. A large variance often signals an opportunity for improvement in the process by finding ways to reduce the process variance. Conduct a

2. Math

Manufacturing A factory manufactures two products, each requiring the use of three machines. The first machine can be used at most 70 hours; the second machine at most 40 hours; and the third machine at most 90 hours. The first

3. Cost Accounting

Incomplete manufacturing costs, expenses, and selling data for two different cases are as follows. Case 1 2 Direct Materials Used \$ 8,300 (g) Direct Labor 3,000 \$ 4,000 Manufacturing Overhead 6,000 5,000 Total Manufacturing Costs

4. Statistics

At a local manufacturing plant, employees must complete new machine set ups within 30 minutes. New machine set-up times can be described by a normal model with a mean of 22 minutes and a standard deviation of four minutes. b. The

1. statistics

At a local manufacturing plant, employees must complete new machine set ups within 30 minutes. New machine set-up times can be described by a normal model with a mean of 22 minutes and a standard deviation of four minutes. a. What

2. yr 8 design technology

Systems and Control- inputs ,process and outputs 1) public address system - input ? 2)table lamp - process ? 3) street lamp - input ? 4)burgular alam - process? 5)doorbell-output-doorbell sounds (ding dong is this right?) 6)car

3. Statistics

An automatic machine in a manufacturing process is operating properly if the length of an important subcomponent is normally distributed with a mean μ = 80 cm and a standard deviation σ = 2 cm. a) Find the probability that the

4. math

The cosat C, in dollars, of operating a concrete-cutting machine is modelled by C=2.2n^2-66n+655, where n is the number of minutes the machine is run. How long must trhe machine run for the operating cost to be at a minimum? What