Problem
R Programming (To be run on R studios)
Round all decimal answers to 4 decimal places. Use R to find all the percentiles, probabilities and confidence intervals.
The number of minutes for app engagement by a tablet user follows a normal distribution with µ = 8.2 minutes, and σ = 1 minute. Suppose, we take a sample of 60 tablet users.
1. What are the mean and standard deviation of the sampling distribution of the sample mean?
2. Find the 90th percentile for the sample mean time for app engagement for a tablet user. Interpret this value in a complete sentence.
3. Find the probabilities that the sample mean is between ±1 standard deviation, ±2 standard deviations, and ±3 standard deviations.
4. Is there a different way to do part (3) that involves not using R, and not using any form of calculations?