Question

R.I.P. Your Storage Assume the number of apps in a smartphone is normally distributed with mean 90 and standard deviation of 25 . In order to answer these questions, we need to define X to talk about probabilities. Define a random variable X and state everything we know about X from the prompt above.

Answer 1

The random variable X represents the number of apps in a smartphone. It follows a normal distribution with a mean (μ) of 90 and a standard deviation (σ) of 25.

Step-by-step explanation:

The given information defines the random variable X as the number of apps in a smartphone, and we know that X is normally distributed with a mean (μ) of 90 and a standard deviation (σ) of 25. This implies that the majority of smartphones are expected to have around 90 apps, and the distribution of the number of apps follows a bell-shaped curve, with most falling within one standard deviation (25 apps) above or below the mean.

In mathematical terms, X ~ N(90, 25), where N represents a normal distribution. This notation indicates that X follows a normal distribution with a mean of 90 and a standard deviation of 25.

Understanding the characteristics of a normal distribution allows us to make probabilistic statements about the number of apps on a smartphone. For instance, we can calculate the probability that a randomly selected smartphone has more than a certain number of apps by standardizing the variable using the z-score formula:
`\(Z = \frac{{X - \mu}}{{sigma}}\)`. With this, we can find the probability using a standard normal distribution table or calculator.

In summary, defining the random variable X and its distribution parameters enables us to analyze and make probabilistic statements about the number of apps on a smartphone based on the normal distribution properties.