Question

What is the probability that a randomly selected male will have a foot length between 8 and 12.5 inches? P(8 < r < 12.5)= ____ or ____%

Answer 1

To find the probability that a randomly selected male will have a foot length between 8 and 12.5 inches, we can use a normal distribution and calculate the area under the curve between the given foot lengths.

Step-by-step explanation:

To find the probability that a randomly selected male will have a foot length between 8 and 12.5 inches, we need to know the distribution of foot lengths in the male population. Let's assume the distribution follows a normal distribution with a mean of 10 inches and a standard deviation of 1 inch.

Then, the probability can be found by calculating the area under the curve between 8 and 12.5 inches. We can use the z-score formula to convert the foot lengths to z-scores and then use a standard normal distribution table or a calculator to find the corresponding probabilities.

Let's calculate the z-scores:

z1 = (8 - 10) / 1 = -2

z2 = (12.5 - 10) / 1 = 2.5

Using the standard normal distribution table or a calculator, we can find that the probability of a randomly selected male having a foot length between 8 and 12.5 inches is approximately 0.9871, or 98.71%.

Answer 2

0.8185 or 81.85%

Step-by-step explanation:

The mean length (μ) of an adult foot is 11 and the standard deviation (σ) is 1.5.

The z score is a measure in statistic used to determine the amount of standard deviation by which the raw score (x) is above or below the mean. If the raw score is above the mean, the z score is positive and if the raw score is below the mean the z sore is negative. It is given by:

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

To calculate the probability that a randomly selected male will have a foot length between 8 and 12.5 inches, we first calculate the z score for 8 inches and then for 12.5 inches.

For 8 inches:

`z=(x-\mu)/(\sigma)=(8-11)/(1.5)=-2`

For 12.5 inches:

`z=(x-\mu)/(\sigma)=(12.5-11)/(1.5)=1`

From the normal distribution table, The probability that a randomly selected male will have a foot length between 8 and 12.5 inches = P(8 < x < 12.5) = P(-2 < z < 1) = P(z < 1) - P(z < -2) = 0.8413 - 0.0228 = 0.8185 = 81.85%