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Question:
If a sample of 2 hammer is selected
(a) find the probability that all in the sample are defective.
(b) find the probability that none in the sample are defective.
Answer:
a
b
Step-by-step explanation:
Given
--- hammers
--- selection
This will be treated as selection without replacement. So, 1 will be subtracted from subsequent probabilities
Solving (a): Probability that both selection are defective.
For two selections, the probability that all are defective is:
Solving (b): Probability that none are defective.
The probability that a selection is not defective is:
For two selections, the probability that all are not defective is:
Answer:
a) The 95% confidence interval for the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.
b) The confidence interval is built from a sample of 48 days. However, we can be 95% sure that for all days, the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.
Step-by-step explanation:
We have the standard deviation for the sample. So we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 48 - 1 = 47
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 47 degrees of freedom(y-axis) and a confidence level of . So we have T = 2.0117
The margin of error is:
M = T*s = 2.0117*2.3 = 4.6
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 7.1 - 4.6 = 2.5 hours of sunlight per day
The upper end of the interval is the sample mean added to M. So it is 7.1 + 4.6 = 11.7 hours of sunlight per day
a) Compute the 95% confidence interval for the mean.
The 95% confidence interval for the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.
b) Explain your confidence interval from part (a) in context.
The confidence interval is built from a sample of 48 days. However, we can be 95% sure that for all days, the mean number of hours per day her solar panel receives direct sunlight is between 2.5 and 11.7.