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.