Question

Mean is 9.25 hours with a standard deviation of 2.5 hours.

You are planning your recharging schedule so that the
probability your phone will die is no more than 5%. After how many
hours should you plan to recharge your phone?

Answer 1

To determine the number of hours you should plan to recharge your phone, find the value that corresponds to a probability of no more than 5% using the mean and standard deviation. Then calculate the value using the z-score formula.

Step-by-step explanation:

To determine the number of hours you should plan to recharge your phone, you need to find the value that corresponds to a probability of no more than 5% in a normal distribution with a mean of 9.25 hours and a standard deviation of 2.5 hours.

First, find the z-score corresponding to a probability of 0.05. Using a z-table or calculator, you can find that the z-score is approximately -1.645.

Next, use the formula z = (x - mean) / standard deviation to find the value of x. Rearranging the formula, x = z * standard deviation + mean. Plugging in the values, x = -1.645 * 2.5 + 9.25 = 5.14.

Therefore, you should plan to recharge your phone after approximately 5.14 hours.