Resolved: "Let us now assume that the length of..."

kenziebabyyy4e

Answered question

2021-11-25

Let us now assume that the length of one year of artic char follows normal distributions with an average of 127 cm and a standard deviation of 16 cm.
a) If an artic char is chosen at random, what is the probability that it is longer than 140 cm?
b) Should the arctic char be in the group of the 5% longest arctic char when itis one year old, how big does it have to be?

Answer & Explanation

Jeffrey Parrish

Beginner2021-11-26Added 15 answers

Step1
Given: mean = 127cm
standard deviation = 16cm
letx be the length of artic char
to find: i) If an artic char is chosen at random, what is the probability that it is longer than 140 cm i.e

P (X > 140)

ii) Should the arctic char be in the group of the 5% longest arctic char when it is one year old, how big does it have tobe.
Step2
Solution:
i)

P (X > 140) = 1 - P (X < 140)

= 1 - P (X < \frac{140 - 127}{16})

= 1 - z (\frac{140 - 127}{16})

= 1 - z (0.8125)

= 1 - 0.791

= 0.209 or 20.9 %

ii)

P (X < a) = 0.95

P (X < \frac{a - 127}{16}) = 0, 95

z value is 1.645 when the p value is 0.95

\frac{a - 127}{16} = 1.645

a = {1.645}^{\cdot} 16 + 127

a = 153.32 c m

Therefore,
probability that it is longer than 140 cm is 20.9%
Should the arctic char be in the group of the 5% longest arctic char when it is one year old, the arc has to be 153.3cm big

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