A bag Contains rubber bands with lengths that are normally distributed with a mean of 6 cm of length, and a standard deviation of 1.5 cm. What is the probability that a randomly selected nail is between 4.5 and 7.5 cm long?

0.68

Step-by-step explanation:

Given

Mean = μ = 6 cm

SD = σ = 1.5 cm

We have to find the z-scores for 4.5 and 7.5

z-score for 4.5 = z_1 = (x-μ) / σ = (4.5-6) / 1.5 = - 1.5/1.5 = - 1

z-score for 4.5 = z_2 = (x-μ) / σ = (7.5-6) / 1.5 = 1.5/1.5 = 1

We have to find area to the left of z-scores

Using the rule of thumb for SD from mean, 68% of data lies between one standard deviation from mean. So the probability of choosing a band with length between 4.5 and 7.5 cm is 0.68 ...