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
