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

Answer: 0.5

Step-by-step 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 : $z=\dfrac{x-\mu}{\sigma}$

For x=70, we have

$z=\dfrac{70-70}{4}=0$

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

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

$P(x\geq70)=P(z\geq0)=1-P(z$

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

Answer 2

Answer:

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

Step-by-step 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: $Z=\frac{x-\mu}{\sigma}$

$Z=\frac{70-70}{4}$

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