Question

Questions 15 and 16 are related 15 Suppose the distribution of sardine lengths is approximately normal...

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

Homework Answers

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)

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