Mathematics: The time until recharge for a battery in a laptop computer under common conditions is normally distributed with mean of 265 minutes and a standard deviation of 50 minutes. a) What is the probability that a battery lasts more than four hours? Enter your answer in accordance to the item a) of the question statement (Round the answer to 3 decimal places.) b) What are the quartiles (the 25% and 75% values) of battery life? 25% value = Enter your answer; 25% value = _ minutes minutes (Round the answer

the 3rd on is correct step-by-step explanation:...

The time until recharge for a battery in a laptop

Ответ:

maxstmichel3868

22.01.2022

Mathematics

a) 0.691 = 69.1% probability that a battery lasts more than four hours

b) 25% value = 231

75% value = 299

c) 183 minutes

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 265, \sigma = 50$