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In: Statistics and Probability

Full-time college students report spending a mean of 30 30 hours per week on academic​ activities,...

Full-time college students report spending a mean of 30 30 hours per week on academic​ activities, both inside and outside the classroom. Assume the standard deviation of time spent on academic activities is 4 4 hours. Complete parts​ (a) through​ (d) below. b. If you select a random sample of 25 25 ​full-time college​ students, there is an 83 83​% chance that the sample mean is less than how many hours per​ week?

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Expert Solution

µ =    30                              
σ =    4                              
n=   25                              
proportion=   0.8300                              
                                  
Z value at    0.83   =   0.954   (excel formula =NORMSINV(   0.83   ) )          
z=(x-µ)/(σ/√n)                                  
so, X=z * σ/√n +µ=   0.954   *   4   / √    25   +   30   =   30.76

If you select a random sample of 25 25 ​full-time college​students, there is an 83 83​% chance that the sample mean is less than 30.76 hours per​ week

orchestra answered 3 years ago
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