19M.1.SL.TZ1.T_11
Consider the following graphs of normal distributions.
At an airport, the weights of suitcases (in kg) were measured. The weights are normally distributed with a mean of 20 kg and standard deviation of 3.5 kg.
In the following table, write down the letter of the corresponding graph next to the given mean and standard deviation.
Find the probability that a suitcase weighs less than 15 kg.
Any suitcase that weighs more than kg is identified as excess baggage.
19.6 % of the suitcases at this airport are identified as excess baggage.
Find the value of .
Markscheme / solution
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
(A1)(A1) (C2)
Note: Award (A1) for each correct entry.
[2 marks]
(M1)
Note: Award (M1) for sketch with 15 labelled and left tail shaded OR for a correct probability statement, P(X < 15).
0.0766 (0.0765637…, 7.66%) (A1) (C2)
[2 marks]
(M1)
Note: Award (M1) for a sketch showing correctly shaded region to the right of the mean with 19.6% labelled (accept shading of the complement with 80.4% labelled) OR for a correct probability statement, P(X > ) = 0.196 or P(X ≤ ) = 0.804.
23.0 (kg) (22.9959… (kg)) (A1) (C2)
[2 marks]