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Facebook provides a variety of statistics on its Web site that detail the growth and popularity of the site.

On average, 28 percent of 18 to 34 year olds check their Facebook profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a standard deviation of five percent.

a. Find the probability that the percent of 18 to 34-year-olds who check Facebook before getting out of bed in the morning is at least 30 .

b. Find the 95th percentile, and express it in a sentence.

Short Answer

Expert verified

(a) The resultant value of P(x≥30)is 0.3446.

(b)The percentage of 18 to 34-year-olds who check their Facebook profiles before getting out of bed in the morning is 95% percent.

Step by step solution

01

Part (a) Step 1: Given information

According to the information provided, Facebook's websites present a number of statistics.

It shows that on average $28 percent of people in the 18 to 34 year old age group check their Facebook before getting out of bed, and that this percentage follows a normal distribution with a standard deviation of $5 percent.

Let X represent the variable that 18 to 34 year olds check Facebook before getting out of bed. X is normally distributed with a mean of 28 and a standard deviation of 5.

X~N(28,5)

02

Part (a) Step 2: Explanation

The necessary probability can now be calculated as follows:

P(X≥30)=1-P(X<30)=1-PX-μσ<30-μσ=1-PZ<30-285=1-P(Z<0.4)

So,

P(X≥30)=1-0.6554Fromstandardnormaltable=0.3446
03

Part (b) Step 1: Given information

According to the information provided, Facebook's websites present a number of statistics.

It shows that on average $28 percent of people in the 18 to 34 year old age group check their Facebook before getting out of bed, and that this percentage follows a normal distribution with a standard deviation of $5 percent.

Let X represent the variable that 18 to 34 year olds check Facebook before getting out of bed. X is normally distributed with a mean of 28 and a standard deviation of 5.

X~N(28,5)

04

Part (b) Step 2: Explanation

The Ti-83 calculator may be used to calculate the 95thpercentile.

Use the Ti-83 calculator's invNorm( ) function for this.

To use invNorm(), choose second, then DISTR, then scroll down to the invNorm option and fill in the required information. After that, press the calculator's ENTER key to get the desired result.

The screenshot is as follows:

Therefore, the 95th percentile is 36.22 percent.

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Most popular questions from this chapter

Kyle’s doctor told him that the z-score for his systolic blood pressure is 1.75. Which of the following is the best interpretation of this standardized score? The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean µ=125and standard deviation σ=14. If X = a systolic blood pressure score then X~N(125,14).

a. Which answer(s) is/are correct?

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