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faust18 [17]
2 years ago
9

Electricity usage data consists of 45 months has a mean number of units consumed is 390.47 per month with a standard deviation o

f 170.5 units per month. Assume that the number of units consumed are approximately normally distributed. Estimate 95% confidence interval for the average monthly electricity consumed units.
Mathematics
1 answer:
neonofarm [45]2 years ago
6 0

Answer:

The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87

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 = 45 - 1 = 44

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 44 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 2.0141

The margin of error is:

M = T*s = 2.0141*170.5 = 343.4

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 390.47 - 343.40 = 47.07 units per month

The upper end of the interval is the sample mean added to M. So it is 390.47 + 343.40 = 733.87 units per month

The 95% confidence interval for the average monthly electricity consumed units is between 47.07 and 733.87

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Miss Berk has 8 pairs of pajama pants and 3 pairs of slippers. Three pairs of the pajama pants are Harry Potter themed and one p
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The probability that both items will be Harry Potter themed is 1/8.

<u>Step-by-step explanation:</u>

Total Number of pajama pants n(P) =8

Total number of slippers n(S)= 3

Number of Harry Potter themed Pajama pants n(H.P)=3

Number of Harry Potter themed slippers n(H.S)=1

We have to determine the probability of selecting pants and slippers that are both Harry Potter themed.

If two events A and B are independent, then the probability of A and B is given by

P(A and B)=P(A)*P(B)

Here the events selecting Harry potter themed pants and selecting harry Potter themed slippers are independent.

P(Harry\ Potter\ pants)=\frac{n(H.P)}{n(P)}

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P(Harry\ Potter\ pants\ and\ Harry\ Potter\ slippers)=P(Harry Potter pants)\times P(Harry potter slippers)

=\frac{3}{8}\times  \frac{1}{3} =\frac{1}{8}

Hence probability of selecting Harry potter themed pants and Harry potter themed slippers is 1/8

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