Question

The battery life of a new rechargeable battery is normally distributed with a mean of 1,450 hours and a standard deviation of 8.5 hours. If one of these new rechargeable batteries is selected at random, what is the probability that its battery life will be between 1,440 and 1,465 hours? Round to the nearest whole number.(1 point)

98%

84%

68%

95%
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Answer 1

Compute z-scores: for 1440, z = (1440−1450)/8.5 = −1.176; for 1465, z = (1465−1450)/8.5 = 1.765.
P(1440 < X < 1465) = Φ(1.765) − Φ(−1.176) ≈ 0.9612 − (1 − 0.8802) = 0.8414 ≈ 84%.

Answer: 84%.