Assume the average weight of an American adult male is 180 pounds with a standard deviation of 34 pounds. The distribution of weights follows a normal distribution. What is the probability that a man weighs exactly 185 pounds?

Answer :

Answer:

Zero is the probability that a man weighs exactly 185 pounds.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 180 pounds

Standard Deviation, σ =  34 pounds

We are given that the distribution of  34 pounds is a bell shaped distribution that is a normal distribution.

Continuous Distribution:

  • A particular random variable will have a probability zero.
  • Thus, it cannot be expressed in a tabular form.
  • A probability density function is defined to give the probability.

Since normal distribution is a continuous distribution, the probability of a particular random variable is zero.

Thus, the probability that a man weighs exactly 185 pounds is zero.

Answer:

Probability that a man weighs exactly 185 pounds = 0.55962 .

Step-by-step explanation:

We are given that the average weight of an American adult male is 180 pounds with a standard deviation of 34 pounds i.e.;

Mean, [tex]\mu[/tex] = 180 pounds          and          Standard deviation, [tex]\sigma[/tex] = 34 pounds

Also, the distribution of weights follows a normal distribution so;

                   Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)

Let X = weight of a man

So, Probability( X = 185 pounds) = P( [tex]\frac{X-\mu}{\sigma}[/tex] = [tex]\frac{185-180}{34}[/tex] ) = P(Z = 0.15) = 0.55962.

The above probability is calculated using z table.

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