Question

Questions 15 and 16 are related
15	Suppose the distribution of sardine lengths is approximately normal with a mean of 4 centimeters and a standard deviation of 0.55 centimeter. Sardines that are too long or too short for a sardine can are ground up for cat food. The range of sizes that can be used in a sardine can is from 3 to 5 centimeters. What fraction of all sardines are ground up for cat food?
a	0.0292
b	0.0688
c	0.1010
d	0.1142
16	In the previous question what is the middle interval that includes 90% of all sardines?
a	3.4	4.6
b	3.3	4.7
c	3.2	4.8
d	3.1	4.9

Answer 1

Solution:-

15) (b) The fraction of all sardines are ground up for cat food is 0.0688.

Mean = 4, S.D = 0.55

x₁ = 3.0

x₂ = 5.0

By applying normal distruibution:-

z₁ = - 1.82

z₂ = 1.82

P( - 1.82 > z > 1.82) = P(z < - 1.82) + P(z > 1.82)

P( - 1.82 > z > 1.82) = 0.034 + 0.034

P( - 1.82 > z > 1.82) = 0.0688

16) (d) The middle interval that includes 90% of all sardines is C.I = (3.1, 4.9).

C.I = 4 + 1.645 × 0.55

C.I = 4 + 0.90475

C.I = (3.095, 4.905)