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galben [10]
3 years ago
15

The number of defective units in a production run of 850 circuit boards are normally distributed with 21 defective units and 3 d

efective units. Find the probability P(17 < X < 25) with the help of the graphing calculator. Round your answer to the nearest integer.
77%

81%

80%

82%

Mathematics
1 answer:
Katen [24]3 years ago
5 0

Answer:

82%

Step-by-step explanation:

We let the random variable X denote the number of defective units in the production run. Therefore, X is normally distributed with a mean of 21 defective units and a standard deviation of 3 defective units.

We are required to find the probability, P(17 < X < 25), that the number of defective units in the production run is between 17 and 25.

This can be carried out easily in stat-crunch;

In stat crunch, click Stat then Calculators and select Normal

In the pop-up window that appears click Between

Input the value of the mean as 21 and that of the standard deviation as 3

Then input the values 17 and 25

click compute

Stat-Crunch returns a probability of approximately 82%

Find the attachment below.

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Answer:

P(X = x) = C_{8,x}.(0.4)^{x}.(0.6)^{8-x}

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Step-by-step explanation:

For each traffic fatality, there are only two possible outcomes. EIther it involved an intoxicated or alcohol-impaired driver or nonoccupant, or it didn't. Traffic fatalities are independent of other traffic fatalities, which means that the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

The probability is .40 that a traffic fatality involves an intoxication or alcohol-impaired driver or nonoccupant.

This means that p = 0.4

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This is P(X = x), in which x is the number of which we want to find the probability. So

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