A study was conducted on the weights of newborn piglets. The weights were normally distributed with a mean μ = 0.76 kg and standard deviation σ = 0.18 kg. If the study involved 5,000 piglets, how many of them weighed more than 0.94 kg? A. 800 B. 600 C. 2500 D. 4200

Question

Anabella Francis

Mathematics

2 February, 18:26

A study was conducted on the weights of newborn piglets. The weights were normally distributed with a mean μ = 0.76 kg and standard deviation σ = 0.18 kg. If the study involved 5,000 piglets, how many of them weighed more than 0.94 kg? A. 800 B. 600 C. 2500 D. 4200

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Avery Madden · Answer 1

A. 800

Step-by-step explanation:

Let the random variable X denote the weight of newborn piglets. We first determine the probability that X is greater than 0.94;

Pr (X>0.94)

We apply the standard normal transformation;

Z = (X-μ) / σ

Pr (X>0.94) = Pr (Z> (0.94-0.76) / 0.18)

= Pr (Z>1)

= 0.1587, from the standard normal tables

To determine the number that weighed more than 0.94 kg, we simply multiply this probability with the number 5000;

5000*0.1587 = 793.5 which is close to 800