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The typical college freshman spends an average of μ=150 minutes per day, with a standard deviation of σ=50 minutes, on social media. The distribution of time on social media is known to be Normal. The proportion of students spending at least 2 hours on social media equals:

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JeanaShupp

Answer: The proportion of students spending at least 2 hours on social media equals 0.7257 .

Step-by-step explanation:

Given : The typical college freshman spends an average of μ=150 minutes per day, with a standard deviation of σ=50 minutes, on social media.

The distribution of time on social media is known to be Normal.

Let x be the number of minutes spent on social media.

Then, the probability that students spending at least 2 hours (2 hours = 120 minutes as 1 hour = 60 minutes) on social media would be:

[tex]P(x\geq120)=1-P(x<120)\\\\=1-P(\dfrac{x-\mu}{\sigma}<\dfrac{120-150}{50})\\\\=1-P(z<-0.6)\ \ [\because z=\dfrac{x-\mu}{\sigma}]\\\\=1-(1-P(z<0.6))\ \ [\because\ P(Z<-z)=1-P(Z<z)]\\\\=P(z<0.6)=0.7257\ \ [\text{By z-table}][/tex]

Hence, the proportion of students spending at least 2 hours on social media equals 0.7257 .

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