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angie249
17.03.2020 •
Mathematics
It is known that 70% of all brand A external hard drives work in a satisfactory manner throughout the warranty period (are "successes"). Suppose that n = 15 drives are randomly selected. Let X = the number of successes in the sample. The statistic X/n is the sample proportion (fraction) of successes. Obtain the sampling distribution of this statistic. [Hint: One possible value X/n is 0.2, corresponding to X = 3. What is the probability of this value (what kind of random variable is X)?] (Round your answers to three decimal places.)
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Ответ:
The probability distribution of
is,
.
Step-by-step explanation:
The random variable X is defined as the number of brand A external hard drives work in a satisfactory manner throughout the warranty period.
The sample selected is of size, n = 15.
The probability of selecting a hard drive that works in a satisfactory manner throughout is, p = 0.70.
Every hard drive works independently of the others.
The random variable X follows a Binomial distribution with parameters n = 15 and p = 0.70.
The probability mass function of X, the binomial random variable is:
The probability distribution of X is shown below.
Now a statistic is defined as:
This statistic is known as the sample proportion.
A Normal approximation to Binomial can be used to approximate the distribution of sample proportion if the following conditions are satisfied:
np ≥ 5n(1 - p) ≥ 5Then the sampling distribution of
follows a Normal; distribution with mean
and standard deviation
.
Check the conditions:
So, the probability distribution of
is,
.
Ответ: