The height of 18-year-old men are approximately normally distributed, with mean of 68 inches and a standard deviation of 3 inches. What is the probability that an 18-year-old man selected at random is between 67 and 69 inches tall? Round your answer to the nearest thousandths place (3 places).
To find the probability that a randomly selected 18-year-old man is between 67 and 69 inches tall, we need to use the concept of the normal distribution and calculate the z-scores.
First, let's calculate the z-score for 67 inches:
z = (x - μ) / σ
where x is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.
For 67 inches:
z = (67 - 68) / 3
z = -1 / 3
z = -0.3333 (rounded to four decimal places)
Next, let's calculate the z-score for 69 inches:
z = (x - μ) / σ
where x is the value we want to find the z-score for, μ is the mean, and σ is the standard deviation.
For 69 inches:
z = (69 - 68) / 3
z = 1 / 3
z = 0.3333 (rounded to four decimal places)
Now, we need to find the probability between these two z-scores using a standard normal distribution table or a calculator.
Using a standard normal distribution table, the probability of being between -0.3333 and 0.3333 is approximately 0.369.
Therefore, the probability that an 18-year-old man selected at random is between 67 and 69 inches tall is 0.369 (rounded to three decimal places).
Use z-scores and a z-table to find your probability.
Formula:
z = (x - mean)/sd
mean = 68
sd = 3
Find two z-values, using 67 and 69 for x.
Next, check a z-table for the probability between the two z-scores.
I hope this will help get you started.