Answer: The required probability is 0.1328.
Step-by-step explanation:
Since we have given that
n = 5
Probability of success = p = defective rate = 3% = 0.03
Probability of failure = q = 1-p = 1 - 0.03 = 0.97
So, we will use "Binomial distribution":
probability that the first defective occurs in the fifth item inspected would be
Hence, the required probability is 0.1328.
Answer:
a)
b)
c)
d)
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
We select a random sample of n=36. And from the central limit theorem we know that the distribution for the sample is given by:
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
Part b
For this case we want this probability:
And we can find this probability on this way:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
Part c
If we apply this formula to our probability we got this:
Part d
For this case we want this probability:
And we can find this probability on this way:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.