The length for loaves of rye bread distributed to local stores by a certain bakery is normally distributed. Table Q2 below shows the length of 30 loaves of rye bread recorded in centimeters.
Table Q2 Length of 30 loaves of rye bread recorded in centimeters
34.713 36.861 38.668
38.671 34.787 35.997
36.393 35.803 33.158
34.616 35.842 34.064
32.990 37.069 37.796
33.422 33.249 34.937
34.990 32.908 34.814
34.816 36.375 36.859
36.152 38.483 32.602
35.521 32.019 38.117
(a) What is the probability that on average, the loaves are longer than 35.525 centimeters?
[5 marks]
(b) What is the probability that on average, the loaves are between 34.323 cm and 36.875 cm in length?
[4 marks]
(c) If specifications require that the mean length of the loaves to be between 35.255 and 36.255 centimeters, what is the probability that a loaf will be rejected?
[6 marks]