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Answer :
Answer:
[tex] \boxed{166\: lbs \: [pounds \: of \: weight]} [/tex]
Step-by-step explanation:
Mean =
Sum of data / # of data
Mean =
(180 lbs + 170 lbs + 168 lbs + 184 lbs + 182 lbs) / (5)
Since the weight of the next doctors appointment is unknown and must equal a mean weight of 175, there will be one more data point and we will let x represent this unknown weight:
175 lbs = (180 lbs + 170 lbs + 168 lbs + 184 lbs + 182 lbs + x lbs) / (5 + 1) →
175 lbs = (884 lbs + x lbs) / (6) →
(884 lbs + x lbs) / (6) = 175 lbs →
(884 lbs + x lbs) / (6) × 6 = 175 lbs × 6 →
884 lbs + x lbs = 1050 lbs →
(884 + x) lbs = (1050) lbs →
(884 + x = 1050) lbs →
(884 + x – 884 = 1050 – 884) lbs →
(x = 1050 – 884) lbs →
x = 166 lbs
_____________________________
166 lbs must be the weight for the mean of these weights to be 175 because:
(180 lbs + 170 lbs + 168 lbs + 184 lbs + 182 lbs + x lbs) / (5 + 1) →
(180 lbs + 170 lbs + 168 lbs + 184 lbs + 182 lbs + 166 lbs) / (5 + 1) →
(1050 lbs) / 6 →
175 lbs
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