Question

How many apps? According to a website, the mean number of apps on a smartphone in the United States is 94. Assume the number of apps is normally distributed with mean 94 and standard deviation 22. What proportion of phones have between 73 and 108 apps? Round the answer to four decimal places. The proportion of phones that have between 73 and 108 apps is

Answer 1

The proportion of smartphones with between 73 and 108 apps is approximately 56.90%, calculated using the Z-scores for these values and the standard normal distribution.

Step-by-step explanation:

To calculate the proportion of smartphones with between 73 and 108 apps, we use the standard normal distribution. With a mean (μ) of 94 and a standard deviation (σ) of 22, we find the Z-scores for 73 and 108:

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Now we look up these Z-scores in the standard normal distribution table or use a Z-score calculator to find the corresponding probabilities. The probability that a Z-score is between -0.9545 and 0.6364 is the difference in the probabilities from the table or calculator:

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Therefore, the proportion of phones that have between 73 and 108 apps is approximately 0.5690 or 56.90% when rounded to four decimal places.