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Given in the question that, The mean number of minutes for app engagement by a table use is$8.2$ minutes. Suppose the standard deviation is one minute. Take a sample size of$70$.

According to the provided facts, the mean number of minutes for app engagement by a tablet user is $8.2$minutes, the standard deviation is $1$minute and the sample size is$70$.

The mean and standard deviation will follow the normal distribution. So, the distribution of sum of ages of tablet users is given as:

$\mathrm{Î\pounds }X~N\left(n{\mathrm{μ}}_X,\sqrt{n}{\mathrm{σ}}_X\right)$

$∑X~N(70×8.2,\sqrt{70}×1)$

$∑X~N(574,8.366)$

Consider $7$hours as $420$minutes and the $10$hours as $600$minutes. To find the probability that the sum of samples lies between $7$hours and$10$hours, use the Ti-83 calculator. For this, click on $2^{\text{nd}}$, then DISTR, and then scroll down to the normcdf option and enter the provided details. After this, click on ENTER button on the calculator to have the desired result. The screenshot is given below:

Therefore, the probability that the sum of samples lies between$7$hours and$10$hours is$0.9991$.

The probability that the sum of samples lies between $7$hours and $10$hours is$0.9991$.

Given in the question that, The mean number of minutes for app engagement by a table use is$8.2$minutes. Suppose the standard deviation is one minute. Take a sample size of $70$.

According to the provided details, the mean number of minutes for app engagement by a tablet user is $8.2$minutes, standard deviation is $1$minute and the sample size is $70$.

The mean and standard deviation will follow the normal distribution. So, the distribution of sum of ages of tablet users is given as:

$∑X−N\left(n{\mathrm{μ}}_X,\sqrt{n}{\mathrm{σ}}_X\right)$

$∑X~N(70×8.2,\sqrt{70}×1)$

$∑X~N(574,8.366)$

To calculate ${84}^{\text{th}}$and ${16}^{\text{th}}$percentile for the sums of sample, use Ti-83 calculator. For this, click on $2^{\text{nd}}$, then DISTR, and then scroll down to the invnorm option and enter the provided details. After this, click on ENTER button on the calculator to have the desired result. The screenshot is given below:

Therefore,$84th$and $16th$ percentile for the sums of sample are respectively $582.31$ and $565.68$ minutes.

$84th$ and $16th$ percentile for the sums of sample are respectively $582.31$ and $565.68$ minutes.