The average battery life of 2800 manufactured cell phones is recorded and normally distributed. the mean battery life is 12 hours with a standard deviation of 1.3 hours. find the number of phones who have a battery life in the 12 to 13.3 range. ∗ *round your answer to the nearest integer. **do not include commas in your answer.

The number of phones is 956

Step-by-step explanation:

* Lets explain how to solve the problem

- The average battery life of 2800 manufactured cell phones is

  recorded and normally distributed

∴ n = 2800

- The mean battery life is 12 hours

∴ μ = 12

- The standard deviation of 1.3 hours

∴ σ = 1.3

- We need P(12 ≤ x ≤ 13.3) to find the number of phones who

  have a battery life in the 12 to 13.3 range

∵ z-score = (x - μ)/σ

∵ x = 12 , μ = 12 , σ = 1.3

∴ z = (12 - 12)/1.3 = 0

- Use the standard normal distribution table

∴ The corresponding area = 0.50000

∵ x = 13.3 , μ = 12 , σ = 1.3

∴ z = (13.3 - 12)/1.3 = 1

- Use the standard normal distribution table

∴ The corresponding area = 0.84134

∴ P(12 ≤ z ≤ 13.3) = 0.84134 - 0.50000 = 0.34134

∵ P(12 ≤ z ≤ 13.3) = P(12 ≤ x ≤ 13.3)

∴ P(12 ≤ x ≤ 13.3) = 0.34134

∵ The number of phones is 2800

∵ The probability of a battery life in the range 12 to 13.3 is 0.34134

∴ The number of phones who have a battery life in this range is

   2800 × 0.34134 = 955.752 ≅ 956 phones

* The number of phones is 956