Each of 14 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 9 of these refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 6 examined that have a defective compressor. (a) Calculate P(X = 4) and P(X < 4). (Round your answers to four decimal places.) P(X = 4) = 0.4196 P(X S 4) = 0.7622 (b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.) 4.7781 (c) Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 25 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately) P(X s 3) than to use the hypergeometric pmf. We can approximate the hypergeometric distribution with the binomial vy distribution if the population size and the number of successes are large. Here n = 25 and p = M/N = 0.1 Approximate P(X S 3) using that method. (Round your answer to three decimal places.) P(X s 3) z 0.768

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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Each of 14 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 9 of these refrigerators have a defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 6 examined that have a defective compressor.

(I have figured out part "a" but need help with "b" and P(X ≤ 3) in "c")

(a)

Calculate

P(X = 4) and P(X ≤ 4).

(Round your answers to four decimal places.)

P(X = 4)

P(X ≤ 4)

(b)

Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.)

(c)

Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 25 randomly selected refrigerators that have defective compressors, describe a less tedious way to calculate (at least approximately)

P(X ≤ 3)

than to use the hypergeometric pmf.

We can approximate the hypergeometric distribution with the distribution if the population size and the number of successes are large. Here

n =

and

p = M/N = .

Approximate

P(X ≤ 3)

using that method. (Round your answer to three decimal places.)

P(X ≤ 3)

≈

Each of 14 refrigerators of a certain type has been returned to a distributor because of an audible, high-pitched, oscillating noise when the refrigerators are running. Suppose that 9 of these refrigerators have a
defective compressor and the other 5 have less serious problems. If the refrigerators are examined in random order, let X be the number among the first 6 examined that have a defective compressor.
(a) Calculate P(X = 4) and P(X < 4). (Round your answers to four decimal places.)
P(X = 4)
0.4196
P(X < 4) =
0.7622
(b) Determine the probability that X exceeds its mean value by more than 1 standard deviation. (Round your answer to four decimal places.)
4.7781
(c) Consider a large shipment of 400 refrigerators, of which 40 have defective compressors. If X is the number among 25 randomly selected refrigerators that have defective compressors, describe a less
tedious way to calculate (at least approximately) P(X < 3) than to use the hypergeometric pmf.
We can approximate the hypergeometric distribution with the binomial
distribution if the population size and the number of successes are large. Here n = 25
and
p = M/N = 0.1
Approximate P(X < 3) using that method. (Round your answer to three decimal places.)
P(X < 3) - 0.768
You may need to use the appropriate table in the Appendix of Tables to answer this question.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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