Question

A total of 500 iPhone 13's are weighed resulting in a mean weight of 174.0 g with a standard deviation 1.6 g. Assuming the weight are normally distributed, what percentage of the iPhone 13's should fall between 172 g and 176g?(a) 10.56%

(b) 38.49%

(c) 39.44%

(d) 76.98%

(e) 78.88%

(f) None of the above

Answer 1

To determine the percentage of iPhone 13's that fall between 172 g and 176 g, we need to calculate the z-scores for these weights and use the standard normal distribution table.

First, we calculate the z-scores:

z1 = (172 - 174) / 1.6 = -1.25

z2 = (176 - 174) / 1.6 = 1.25

Next, we look up the corresponding cumulative probabilities in the standard normal distribution table:

P(z < -1.25) = 0.1056

P(z < 1.25) = 0.8944

To find the percentage between 172 g and 176 g, we subtract the lower cumulative probability from the higher cumulative probability:

P(172 < x < 176) = P(z < 1.25) - P(z < -1.25) = 0.8944 - 0.1056 = 0.7888

Therefore, the percentage of iPhone 13's that should fall between 172 g and 176 g is 78.88%.

The correct option is (e) 78.88%.