Question

In: Statistics and Probability

The inside diameter of a piston ring is normally distributed with a mean of 10 cm...

The inside diameter of a piston ring is normally distributed with a mean of 10 cm and a standard deviation of 0.04 cm.

  1. What is the probability that a piston ring will have an inside diameter less than 10.075 cm?
  2. What is the probability that a piston ring will have an inside diameter between 9.94 and 10.045 cm?
  3. What proportion of rings will have inside diameters exceeding 10.066 cm?
  4. Suppose that five piston rings are randomly selected. What is the probability that the diameters of exactly four of the five will exceed 10.066 cm?
  5. You continue selecting piston rings from a large number until you find 3 that exceed 10.066 cm. What is the probability that you check exactly 15 rings?

Solutions

Expert Solution

a) P(X < 10.075)

= P((X - )/ < (10.075 - )/)

= P(Z < (10.075 - 10)/0.04)

= P(Z < 1.88)

= 0.9699

b) P(9.94 < X < 10.045)

= P((9.94 - )/ < (X - )/ < (10.045 - )/)

= P((9.94 - 10)/0.04 < Z < (10.045 - 10)/0.04)

= P(-1.5 < Z < 1.13)

= P(Z < 1.13) - P(Z < -1.5)

= 0.8708 - 0.0668

= 0.8040

c) P(X > 10.066)

= P((X - )/ > (10.066 - )/)

= P(Z > (10.066 - 10)/0.04)

= P(Z > 1.65)

= 1 - P(Z < 1.65)

= 1 - 0.9505

= 0.0495

d) n = 5

   p = 0.0495

It is a binomial distribution.

P(X = x) = nCx * px * (1 - p)n - x

P(X = 4) = 5C4 * (0.0495)^4 * (1 - 0.0495)^1 = 0.00003

e) Probability = 14C2 * (0.0495)^2 * (1 - 0.0495)^12 * 0.0495 = 0.0060


Related Solutions

The inside diameter of a randomly selected piston ring is a random variable with mean value...
The inside diameter of a randomly selected piston ring is a random variable with mean value 11 cm and standard deviation 0.06 cm. (a) If X is the sample mean diameter for a random sample of n = 16 rings, where is the sampling distribution of X centered and what is the standard deviation of the X distribution? (Enter your standard deviation to five decimal places.) center     cm standard deviation     cm (b) Answer the questions posed in part (a) for...
The inside diameter of a randomly selected piston ring is a random variable with mean value...
The inside diameter of a randomly selected piston ring is a random variable with mean value 15 cm and standard deviation 0.07 cm. Suppose the distribution of the diameter is normal. (Round your answers to four decimal places.) (a) Calculate P(14.99 ≤ X ≤ 15.01) when n = 16. P(14.99 ≤ X ≤ 15.01) = (b) How likely is it that the sample mean diameter exceeds 15.01 when n = 25? P(X ≥ 15.01) =
Historical Data shows that the diameter of current piston is a normally distributed random variable with...
Historical Data shows that the diameter of current piston is a normally distributed random variable with mean of 12 centimeters and a standar deviation of 0.06 centimeters. 1.if we use 46 ramdomly selected rings and calculate Xbar (average) , what is the probability of having and Xbar greater than 12.01 centimeters? Use original value of standard deviation. 2. Assume you take 40 rings and put them side by side in a line, what is the probability that the length of...
. A steam main (outside diameter of 16.8 cm and inside diameter of 15.4 cm) is...
. A steam main (outside diameter of 16.8 cm and inside diameter of 15.4 cm) is covered with 5-cm of high temperature insulation (k = 0.095 W/m. K) and 3.8 cm of lower temperature insulation (k = 0.07W/m. K). Calculate the heat loss from 150 m pipe assuming that inner and outer surface temperatures of the insulation are 450 and 30 °C, respectively. Also determine the temperature at the interface between two layers of insulation (10 points).
A wooden ring whose mean diameter is 14.5 cm is wound with a closely spaced toroidal...
A wooden ring whose mean diameter is 14.5 cm is wound with a closely spaced toroidal winding of 615 turns. Compute the magnitude of the magnetic field at the center of the cross section of the windings when the current in the windings is 0.640 A .
The diameter of a brand of tennis balls is approximately normally​ distributed, with a mean of...
The diameter of a brand of tennis balls is approximately normally​ distributed, with a mean of 2.58 inches and a standard deviation of .04 inch. A random sample of 11 tennis balls is selected. Complete parts​ (a) through​ (d) below. a. What is the sampling distribution of the​ mean? A.Because the population diameter of tennis balls is approximately normally​ distributed, the sampling distribution of samples of size 11 will be the uniform distribution. B.Because the population diameter of tennis balls...
The diameter of a brand of tennis balls is approximately normally? distributed, with a mean of...
The diameter of a brand of tennis balls is approximately normally? distributed, with a mean of 2.79 inches and a standard deviation of 0.05 inch. A random sample of 10 tennis balls is selected. Complete parts? (a) through? (d) below. a. What is the sampling distribution of the? mean? A.Because the population diameter of tennis balls is approximately normally? distributed, the sampling distribution of samples of size 10 cannot be found. B.Because the population diameter of tennis balls is approximately...
The diameter of a brand of tennis balls is approximately normally distributed, with a mean of...
The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a population standard deviation of .03 inch. If you select a random sample of 9 tennis balls, (a) What is the standard error of the mean? (b) What is the probability that the sample mean is less than 2.61 inches? (c) What is the probability that the sample mean is between 2.62 and 2.64 inches? (d) Between what two values symmetrically...
The diameter of a brand of tennis balls is approximately normally​ distributed, with a mean of...
The diameter of a brand of tennis balls is approximately normally​ distributed, with a mean of 2.69 inches and a standard deviation of 0.05 inch. A random sample of 10 tennis balls is selected. Complete parts​ (a) through​ (d) below. b. What is the probability that the sample mean is less than 2.68 ​inches? c.What is the probability that the sample mean is between 2.67 and 2.70 ​inches? d.  The probability is 71% that the sample mean will be between what...
The diameter of a brand of tennis balls is approximately normally​ distributed, with a mean of...
The diameter of a brand of tennis balls is approximately normally​ distributed, with a mean of 2.58 inches and a standard deviation of 0.03 inch. A random sample of 11 tennis balls is selected. The probability is 69% that the sample mean will be between what two values symmetrically distributed around the population​ mean? (Round to two decimal places). The lower bound is ___ inches, the upper bound is ___ inches.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT