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Answer:
a) the percentage of amounts that are between $36.17 and $44.60 is 49.87%
b.) Therefore the percentage of amounts that are between $41.79 and $47.41 is 68.27%
c) Therefore percentage of amounts that are at least $38.98 = 97.72%
d) The two values will approximately 95% of the amounts be $39.1 and $50.1
Step-by-step explanation:
i) In a recent survey of 655 working Americans, ages 25 - 34, the average weekly amount spent on lunch was $44.60 with a standard deviation of $2.81
ii) mean = $44.60
iii) standard deviation = $2.81
a) Estimate the percentage of amounts that are between $36.17 and $44.60.
therefore we have to find P($36.27 < X < $44.60) or
P(( (36.17 - 44.60)/2.81) < z < ( (44.60 - 44.60)/2.81)) = P(-3 < Z < 0)
therefore P(-3 < Z < 0) = P(Z < 0) - P( Z < -3) = 0.4987
Therefore the percentage of amounts that are between $36.17 and $44.60 is 49.87%
b)estimate the percentage of amounts that are between $41.79 and $47.41.
P($41.79 < X < $47.41) or
P(( (41.79 - 44.60)/2.81) < z < ( (47.41 - 44.60)/2.81)) = P(-1 < Z < 1)
therefore P(-1 < Z < 1) = P(Z < 1) - P( Z < -1) = 0.6827
Therefore the percentage of amounts that are between $41.79 and $47.41 is 68.27%
c)Estimate the percentage of amounts that are at least $38.98.
therefore we have to find
P(X ≥ $38.98) or
P(z ≥ (38.98 - 44.6)/2.81 ) = P( Z ≥ -2)
therefore we have to find 1 - P(Z < -2) = 1 - 0.0228 = 0.9772
Therefore percentage of amounts that are at least $38.98 = 97.72%
d.) Between what two values will approximately 95% of the amounts be?
The two values will approximately 95% of the amounts be $39.1 and $50.1
