Question

Solution of the average life of a bread-making machine is 7 years, with a standard deviation of 1 year. Assuming that the lives of these machines follow approximately a normal distribution, find: (a) the probability that the mean life of a random sample of 9 such machines falls between 6.4 and 7.2 years; (b) the value of x to the right of which 15% of the means computed from random samples of size9 would fall

Answer 1

Answer:

1/3

Step-by-step explanation:

Z score =  (value - Mean) / Standard deviation

Mean = 7

Standard deviation = 1

Z score for 6.4  =  (6.4 -7)/1  = -0.6  

Z score for for 7.2  =  (7.2 - 7)/1 = 0.2

Results between Z score for -0.6  & 0.2  ( Z score reference sheets attached)

= 57.93 - 27.43  =  30.5 %

30.5 % of 9 =  (30.5/100)* 9 = 2.745  = 3

Probability that the mean life of a random sample of 9 such machines falls between 6.4 and 7.2 years = 3/9  = 1/3