The length of time, M hours that a phone battery will work before it needs recharging is normally distributed with a mean of 90 hours, and a standard deviation of 10 hours. Find the interquartile range for this distribution.

The interquartile range is between 83.25 hours and 96.75 hours

Step-by-step explanation:

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

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

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:

Find the interquartile range for this distribution.

That is, the middle 50%, from the 25th to the 75th percentile.

25th percentile:

X when Z has a pvalue of 0.25. So X when Z = -0.675

75th percentile:

X when Z has a pvalue of 0.75. So X when Z = 0.675

The interquartile range is between 83.25 hours and 96.75 hours

the range is 19

step-by-step explanation:

the range is biggest number minus the smallest, so in this case it would be

41 - 22 = 19