Question

The lifespan of a certain electronic toy is normally distributed, with a mean of 3000 hours and a standard deviation of 35 hours. Use a standard normal distribution table or a graphing calculator to find the proportion of toys that have a lifespan between 2920 hours and 2945 hours.

a) 0.0792

b) 0.2154

c) 0.3456

d) 0.1590

Answer 1

To find the proportion of toys that have a lifespan between 2920 hours and 2945 hours, use the z-score formula to standardize the values and then find the probabilities using a standard normal distribution table or a graphing calculator.

Step-by-step explanation:

To find the proportion of toys that have a lifespan between 2920 hours and 2945 hours, we need to find the area under the normal distribution curve between these two values.

First, we need to standardize the values using the z-score formula: z = (x - mean) / standard deviation.

For 2920 hours: z = (2920 - 3000) / 35 = -2.29. For 2945 hours: z = (2945 - 3000) / 35 = -1.57.

Next, we can find the probabilities using a standard normal distribution table or a graphing calculator. The probability of toys having a lifespan between 2920 hours and 2945 hours is the difference between the two probabilities of each z-score: P(-2.29 < z < -1.57).

Using a standard normal distribution table, the proportion is approximately 0.1590. Therefore, the correct answer is d) 0.1590.