The anual commissions earned by sales reps. ofmachine products Inc. a manufactur

Question

The anual commissions earned by sales reps. ofmachine products Inc. a manufacture of light machinery, follow thenormal distribution. the mean yearly amount earned is $40,000 &the standard deviation is $5000.    
a.. what percent of the sales representatives earn more than$42,000 per yr. b. what percent of the sales repsearned between $32,000 & 42,000? c.   what percent of the sales repearn between $32,000 & 35,000? d. the sales manager wants to award thesales reps. who earn the largest commissions a bonusof$1,000, he can award a bonus to 20 % of the reps. what isthe cut off point between those who earned a bonus & those whodid not? also, we want to estimate the populations mean within 5, with a 99 % level of confidence. the populationstandard deviation is estimated to be 15. How large a sampleis required? The anual commissions earned by sales reps. ofmachine products Inc. a manufacture of light machinery, follow thenormal distribution. the mean yearly amount earned is $40,000 &the standard deviation is $5000.    
a.. what percent of the sales representatives earn more than$42,000 per yr. b. what percent of the sales repsearned between $32,000 & 42,000? c.   what percent of the sales repearn between $32,000 & 35,000? d. the sales manager wants to award thesales reps. who earn the largest commissions a bonusof$1,000, he can award a bonus to 20 % of the reps. what isthe cut off point between those who earned a bonus & those whodid not? also, we want to estimate the populations mean within 5, with a 99 % level of confidence. the populationstandard deviation is estimated to be 15. How large a sampleis required? we want to estimate the populations mean within 5, with a 99 % level of confidence. the populationstandard deviation is estimated to be 15. How large a sampleis required?

Explanation / Answer

Let X be the yearly amount earned by a sales representative. ThenX~N(40000,5000) Z will denote the standard normal distribution, Z~N(0,1) a) P(X>42000) = 1 - P(X

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