It is generally believed that electrical problems affect about 14% of new cars. An automobile mechanic conduct?
Question by Brian: It is generally believed that electrical problems affect about 14% of new cars. An automobile mechanic conduct?
It is generally believed that electrical problems affect about 14% of new cars. An automobile mechanic conducts diagnostic
tests on 128 new cars on the lot.
Keywords: Distribution of Sample Proportion, Z scores
1) What is the distribution of sample proportion?
2) What is the probability that in this group over 18% of the new cars will be found to have electrical problems?
Best answer:
Answer by M
1) ANSWER: MEAN = 0.14 * 128 = 18, STANDARD DEVIATION = SQRT(0.14 * 128 * 0.86) = 3.93
2) ANSWER: ANSWER: The probability of the sample greater than 0.18 = 0.12 (1 – 0.88)
Why???
NORMAL DISTRIBUTION, PROPORTION, STANDARDIZED VARIABLE z, PROBABILITY “LOOK-UP”
STANDARDIZED VARIABLE: z = (p^ – p)/(√[p*(1 - p)/n])
= (0.18 – 0.14)/(√[0.14 * (1 - 0.14)/128]) =1.18
SAMPLE PROPORTION: p^ = 0.18
POPULATION MEAN: p = 0.14
SAMPLE SIZE: n = 128
SIGNIFICANT DIGITS = 2
The Table for Standard Normal Distribution is organized as a cummulative ‘area’ from the LEFT corresponding to the STANDARDIZED VARIABLE z. The Standard Normal Distribution is also symmetric (called a ‘Bell Curve’) which means its an interpretive procedure to Look-Up the ‘area’ from the Table. For STANDARDIZED VARIABLE z = 1.18 the corresponding LEFT ‘area’ = 0.88. And due to Table’s cummulative nature, the corresponding RIGHT ‘area’ = 1 – 0.88
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