The technical team of a university would like to perform an analysis on pre-recorded lecture videos. Let X be the video length in minutes. The value of X is collected for a random sample of 85 videos, and the results obtained are summarized in the table below. The corresponding probabilities computed using ī = 50 and s = 15 are also given in the table. Length (min), x < 35 35 – 45 45 – 55 55 – 65 > 65 - Observed frequencies, O 18 30 18 13 Probabilities 0.1587 0.2108 0.2610 0.2108 0.1587 Perform a x goodness-of-fit analysis with a significance level of 0.05 to test the hypothesis that these data follow a normal distribution. Use 4 decimal places for the intermediate steps.

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The technical team of a university would like to perform an analysis on pre-recorded lecture
videos. Let X be the video length in minutes. The value of X is collected for a random sample
of 85 videos, and the results obtained are summarized in the table below. The corresponding
probabilities computed using = 50 and s = 15 are also given in the table.
Length (min), x
< 35
35 – 45 | 45 – 55
55 – 65
> 65
Observed frequencies, O
18
30
18
13
Probabilities
0.1587
0.2108
0.2610
0.2108
0.1587
Perform a x goodness-of-fit analysis with a significance level of 0.05 to test the hypothesis
that these data follow a normal distribution. Use 4 decimal places for the intermediate steps.
Transcribed Image Text:The technical team of a university would like to perform an analysis on pre-recorded lecture videos. Let X be the video length in minutes. The value of X is collected for a random sample of 85 videos, and the results obtained are summarized in the table below. The corresponding probabilities computed using = 50 and s = 15 are also given in the table. Length (min), x < 35 35 – 45 | 45 – 55 55 – 65 > 65 Observed frequencies, O 18 30 18 13 Probabilities 0.1587 0.2108 0.2610 0.2108 0.1587 Perform a x goodness-of-fit analysis with a significance level of 0.05 to test the hypothesis that these data follow a normal distribution. Use 4 decimal places for the intermediate steps.
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