Question 2.

(a) (6 points) The price of one kilogram of ground meat is distributed normally withmean 22.4 TL and standard deviation of 2.7 TL. What is the probability that the price paid for1 kg of ground meat is less than 18.5 TL ?

Solution:Let X be the price of one kilogram of ground meat.

X s N(22:4; 2:7)) Z = X�22:42:7 s N(0; 1)

P (X < 18:5) = P�X�22:42:7 < 18:5�22:4

2:7

�= P (Z < �1:44)

P (Z < �1:44) = 0:5� P (0 < Z < 1:44) = 0:5� 0:4251 = 0:0749~=0:075

(b) (7 points) The amount of chocolate that women over 30 eat per week is normallydistributed with mean of 422 gr., and standard deviation of 109 gr.55% of women over 30 eat more than how many grams of chocolate per week?

Solution:Let Y be the amount of chocolate that women over 30 eat per week.

Y s N (422; 109)

P (Y > K) = 0:55 , K =?

P�Y�422109 > K�422

109

�= 0:55

From Z-table K�422109 = �0:13) K = 407:83

(c) (7 points) 78% of all Swedes sleep less than 6 hours per day in the summer. If the meannumber of hours a Swede sleeps in the summer is 5.2 hours, what is the standard deviation ofthe number of hours per day a Swede sleeps in the summer?

Solution:Let X be the number of hours that Swedes sleep per day in summer.

X s N (5:2; �)

P (X < 6) = 0:78) P�X�5:2� < 6�5:2

�

�= 0:78

) P�Z < 6�5:2

�

�= 0:78

From Z-table 6�5:2� = 0:77) � = 1:039~=1:04

1