known to be normally distributed with a standard deviation of $2.50. The last seven times John has taken a taxi from Logan to downtown Bosto

Question

known to be normally distributed with a standard deviation of $2.50. The last seven times John has taken a taxi from Logan to downtown Boston, the fares have been $22.10, $23.25, $21.35, $24.50, $21.90, $20.75, and $22.65. Construct a 95% confidence interval for the population mean.

in progress 0
Elliana 2 weeks 2021-09-15T07:21:16+00:00 1 Answer 0

Answers ( )

    0
    2021-09-15T07:22:30+00:00

    Answer:

    The 95% confidence interval for the population mean is between $20.51 and $24.21.

    Step-by-step explanation:

    The first step to find this question is find the sample mean

    \mu_{x} = \frac{22.10 + 23.25 + 21.35 + 24.50 + 21.90 + 20.75 + 22.65}{7} = 22.36

    Confidence interval

    We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

    \alpha = \frac{1-0.95}{2} = 0.025

    Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

    So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

    Now, find M as such

    M = z*\frac{\sigma}{\sqrt{n}}

    In which \sigma is the standard deviation of the population and n is the size of the sample.

    M = 1.96*\frac{2.5}{\sqrt{7}} = 1.85

    The lower end of the interval is the sample mean subtracted by M. So it is 22.36 – 1.85 = $20.51

    The upper end of the interval is the sample mean added to M. So it is 22.36 + 1.85 = $24.21

    The 95% confidence interval for the population mean is between $20.51 and $24.21.

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )