The marks obtained by 1000 students is normally distributed with mean 78 % and standard deviation 11%. Determine 6 i) how many get more than 90%. Ii) how many students get between 75% and 95%
Answers
138 Students Get more than 90% & 546 Students Get Between 75% & 95% when Mean = 78% & SD = 11% of 1000 students
Step-by-step explanation:
Mean =78 %
Standard Deviation = 11 %
Value = 90 %
Z = (Value - Mean) / SD
Z = ( 90 - 78)/11
Z = 12/11
Z = 1.091
Z = 1.091 will give 86.23%
more than 90%. = 100 - 86.23 = 13.77%
13.77% of 1000 = 137.7
138 Students Get more than 90%
Between 75% & 95%
Z = ( 75 - 78)/11 = - 3/11 = -0.2727 = 39.25%
Z = (95 - 78)/11 = 17/11 = 1.5455 =93.89%
Between 75% & 95% = 93.89% - 39.25% = 54.64 %
54.64 % of 1000 = 546.4
546 Students Get Between 75% & 95%
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