Question

According to a website, the mean number of apps on a smartphone in the United States is 84. Assume the number of apps is normally distributed with mean 84 and standard deviation 23. What proportion of phones have more than 78 apps Round the answer to four decimal places. The proportion of phones that have more than 78 apps is D.

Answer 1

To find the proportion of phones that have more than 78 apps, use the z-score formula and a standard normal distribution table or calculator. The proportion is 0.3974.

Step-by-step explanation:

To find the proportion of phones that have more than 78 apps, we need to calculate the area under the normal distribution curve to the right of 78. We can use z-scores to do this.

First, calculate the z-score for 78 using the formula: z = (x - μ) / σ. In this case, x is 78, μ is 84, and σ is 23. Plugging in the values, we get: z = (78 - 84) / 23 = -0.26.

Next, we can use a standard normal distribution table or calculator to find the proportion of phones with more than 78 apps. The proportion is equal to 1 minus the cumulative probability to the left of -0.26. Using a normal distribution table or calculator, we find that this probability is approximately 0.6026. Therefore, the proportion of phones with more than 78 apps is 1 - 0.6026 = 0.3974, rounded to four decimal places.