Final answer:
To determine the probability of the given statistic and the 95th percentile, one would use z-scores and the standard normal distribution, applying the mean of 28 percent and the standard deviation of 5 percent.
Step-by-step explanation:
The question pertains to the calculation of probabilities and percentiles within a normal distribution which is a topic in statistics, a branch of mathematics. To answer this question:
- To find the probability that the percentage of 18- to 34-year-olds who check their social media profiles before getting out of bed in the morning is at least 30, one would calculate the z-score for 30 percent and then consult the standard normal distribution table, or use a calculator with a normal distribution function to determine the area to the right of this z-score.
- To find the 95th percentile, you would look for a z-score that corresponds to 0.95 in the standard normal distribution table (or use an appropriate statistical tool) and then convert this z-score back to a percentage using the mean and standard deviation of the distribution.
It is essential to have a good understanding of statistics to perform these calculations and interpret the results accurately. The standard deviation and normal distribution are key concepts in this scenario.