A stem-and-leaf plot for the number of touchdowns scored by all Division 1 footb
ID: 3315897 • Letter: A
Question
A stem-and-leaf plot for the number of touchdowns scored by all Division 1 football teams is shown below. Complete parts (a) through (c) a) If a team is selected at random, find the probability the team scored at least 31 touchdowns 13 4 5788 Key 115-15 20 1223457889 3001112233445577789 4001223455556 7889 50 235578 61 36 7 Round to three decimal places as needed) ) If a team is selected at random, find the probability the team scored between 40 49 touchdowns inclusive Round to three decimal places as needed) (c) If a team is selected at random, find the probability the team scored more than 78 touchdowns. Are any of these events unusual? Round to three decimal places as needed ) Are any of these events unusual? Select all the unusual events below lI A. Scoring between 40 and 49 touchdowns inclusive is unusual. B. Scoring at least 31 touchdowns is unusual. C. Sconng more than 78 touchdowns is unusual D. None of the events are unusual. Click to select your answer(s).Explanation / Answer
The scores are
13, 14 15, 17, 18, 18, 20, 21, 22, 22, 23, 24, 25, 27, 28, 28, 29, 30, 30, 31, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 37, 37, 37, 38, 39, 40, 40, 41, 42, 42, 43, 44, 45, 45, 45, 45, 46, 47, 48, 48, 49, 50, 52, 53, 55, 55, 57, 58, 61, 63, 66, 67, 7, 87
n = 64
Mean = 37.719
Standard deviation = 14.974
A) P(X > 30) = P((x - mean)/Sd) > (30 - mean)/SD)
= P(Z > (30 - 37.719)/14.974)
= P(Z > -0.52)
= 1 - P(Z < -0.52)
= 1 - 0.3015 = 0.6985
B) P(40 < x < 49) = P(40 - mean)/SD) < (x - mean) /SD) < (30 - mean)/SD)
= P((40 - 37.719)/14.974) < Z < (49 - 37.719)/14.974)
=P(0.15 < Z < 0.75)
= P(Z < 0.75) - P(Z < 0.15)
= 0.7734 - 0.5596
= 0.2138
C) P(X > 78) = P((x - mean)/SD > (78 - mean)/SD)
= P(Z > (78 - 37.719)/14.974)
= P(Z > 2.69)
= 1 - P(Z < 2.69)
= 1 - 0.9964
= 0.0036
Option-C) scoring more than 78 touchdowns is unusual.
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