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A Hollywood film producer is working on a new action film. She wants to estimate the true mean length of action films that have appeared in theatres during the past decade. She randomly selects 30 films and records the run time of each. The average time was 119 minutes with a standard deviation of 21.5 minutes.
Construct a 95% confidence interval that estimates the true mean length of action films over the past decade.
3. Do.
Calculate the 95% confidence interval.
(97.5, 140.5)
(110.83, 127.16)
(110.97, 127.03)
(110.58, 127.43)

Respuesta :

raphealnwobi

The Confidence interval is between 111.31 minutes and 126.69 minutes

Confidence interval

Given that:

Mean (μ) = 119, standard deviation (σ) = 21.5, sample size (n) = 30

Confidence (C) = 95% = 0.95

  • α = 1 - C = 0.05; α/2 = 0.025

The z score of α/2 is the same as the z score of 0.475 (0.5 - 0.025) which is equal to 1.96

The margin of error (E) is:

  • [tex]E=z_\frac{\alpha}{2} *\frac{\sigma}{\sqrt{n} } =1.96*\frac{21.5}{\sqrt{30} } =7.69[/tex]

Confidence interval = (μ ± E) = (119 ± 7.69) = (111.31, 126.69)

The Confidence interval is between 111.31 minutes and 126.69 minutes

Find out more on Confidence interval at: https://brainly.com/question/15712887

Answer:

110.97, 127.03

Step-by-step explanation:

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