Question

For this year's fundraiser, students at a certain school who sell at least 75 magazine subscriptions win a prize. If the fourth grade students at this school sell an average (arithmetic mean) of 47 subscriptions per student, the sales are normally distributed, and have a standard deviation of 14, then approximately what percent of the fourth grade students receive a prize

Answer 1

Answer:

The percentage is  k  =  2.3%

Step-by-step explanation:

From the question we are told that

  The  population mean is  $\mu = 47$

    The  standard deviation is  $\sigma = 14$

Given that the sales are normally distributed and that students at a certain school who sell at least 75 magazine subscriptions win a prize then the  percent of the fourth grade students receive a prize is mathematically represented as

     $P(X > 75) = P(\frac{X - \mu }{\sigma } > \frac{75 - \mu }{\sigma })$

Generally

     $\frac{X - \mu }{\sigma } = Z (The \ standardized \ value \ of \ X )$

So

   $P(X > 75) = P(Z > \frac{75 - 47 }{14 })$

   $P(X > 75) = P(Z > 2)$

From the standardized normal distribution table  

      $P(Z > 2) =0.023$

=>   $P(X > 75) = 0.023$

The  percentage of the fourth grade students receive a prize is  

  k =  0.023 * 100

   k  =  2.3%