Answer:
1) 78 and 82
2)76 and 84
3)74 and 86
Explanation:
1)
Given
mean, x= 80
standard deviation, sd= 2
given percentage of class= 68%
now as per the properties of normal distribution:
-68% of the scores will lie within one standard deviation, sd of the mean, x
i.e. between x-sd and x+sd
Putting values in above we get:
x-sd= 80-2 = 78
x+sd=80+2= 82
Hence about 68% of the class would score between 78 and 82
2)Given
mean, x= 80
standard deviation, sd= 2
given percentage of class= 95%
now as per the properties of normal distribution:
-95% of the scores will lie within 2 standard deviation, sd of the mean, x
i.e. between x-2sd and x+2sd
Putting values in above we get:
x-sd= 80-2(2) = 80-4 = 76
x+sd=80+2(2)= 80+4 = 84
Hence about 95% of the class would score between 76 and 84
3)Given
mean, x= 80
standard deviation, sd= 2
given percentage of class= 99%
now as per the properties of normal distribution:
-99% of the scores will lie within 3 standard deviation, sd of the mean, x
i.e. between x-sd and x+sd
Putting values in above we get:
x-sd= 80-3(2) = 80-6 = 74
x+sd=80+3(2)= 80+6 = 86
Hence about 99% of the class would score between 74 and 86!