Two non-simultaneous events have an equal likelihood of occurring (50%). If the events are independent of each other, what is th
2 answers:
Answer: Probability that they will both occur is 25%.
Step-by-step explanation:
Since we have given that
There are two non simultaneous events.
Probability of each event = 50%
Since both are independent to each other.
Let A and B be two events.
We need to find the probability that they will both occur i..e P(A∩B).
As we know the rule of independence of events:
Hence, Probability that they will both occur is 25%.
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Answer:
The 99% confidence interval is given by ($144.677;$155.323)
We are confidenct at 99% that the true mean for the reapir cost of refrigerators is between 144.677 and 155.323.
Step-by-step explanation:
1) Notation and definitions
n=60 represent the sample size
represent the sample mean
represent the sample standard deviation
m represent the margin of error
Confidence =99% or 0.99
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
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".
2) Calculate the critical value tc
In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 99% of confidence, our significance level would be given by and
. The degrees of freedom are given by:
We can find the critical values in excel using the following formulas:
"=T.INV(0.005,59)" for
"=T.INV(1-0.005,59)" for
The critical value
3) Calculate the margin of error (m)
The margin of error for the sample mean is given by this formula:
4) Calculate the confidence interval
The interval for the mean is given by this formula:
And calculating the limits we got:
The 99% confidence interval is given by ($144.677;$155.323)
We are confidenct at 99% that the true mean for the reapir cost of refrigerators is between 144.677 and 155.323.