Question

Adult male heights have a normal probability distribution with a mean of 70 inches and a standard deviation of 4 inches. What is the probability that a randomly selected male is more than 70 inches tall? Enter you answer in decimal form, e.g. 0.68, not 68 or 68%.

Answer 1

The probability that a randomly selected male is more than 70 inches tall is 0.5

Explanation:

Mean height of adults =
`\mu = 70 inches`

Standard deviation =
`\sigma = 4 inches`

We are supposed to find the probability that a randomly selected male is more than 70 inches tall i.e. P(x>70)

Formula:
`Z=(x-\mu)/(\sigma)`

`Z=(70-70)/(4)`

Z=0

So, p value at z=0 is 0.5

So, P(x>70)=1-P(x<70)=1-0.5 =0.5

Hence the probability that a randomly selected male is more than 70 inches tall is 0.5

Answer 2

Answer: 0.5

Explanation:

Given : Adult male heights have a normal probability distribution .

Population mean :
`\mu = 70 \text{ inches}`

Standard deviation:
`\sigma= 4\text{ inches}`

Let x be the random variable that represent the heights of adult male.

z-score :
`z=(x-\mu)/(\sigma)`

For x=70, we have

`z=(70-70)/(4)=0`

Now, by using the standard normal distribution table, we have

The probability that a randomly selected male is more than 70 inches tall :-

`P(x\geq70)=P(z\geq0)=1-P(z<0)=1-0.5=0.5`

Hence, the probability that a randomly selected male is more than 70 inches tall = 0.5