The director of development at the Richman Children’s Science Museum has recentl

Question

The director of development at the Richman Children’s Science Museum has recently collected data on donations for the past several years. She finds that the data are normally distributed with a mean of $51 and a standard deviation of $14. The director’s ideal point for a minimum donation is $60.

(a) What percentage of individual donations are less than $60?

(b) What percentage of individual donations are $60 or more?

(c) The director’s long-term goal for an average individual donation is at least $80. Based on the current percentage of donations that meet that goal, does achieving this goal seem reasonable in the immediate future?

Explanation / Answer

for $60. the z value is (60-51)/14=0.64

a) P(x<60)=P(z<0.64) . From normal distribution table, this gives 0.7389

b)P(x>=60)=1-P(x<60)=1-0.7389=0.2611

c)P(x>=80) has z value of (80-51)/14 =2.07

which gives the probability as 1-0.9808=0.0192

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