Question

The next two questions (39 and 40) refer to the following: Percentage scores in a large Math class follow a normal distribution with mean 60 and standard deviation 12. Percentage scores in a large Chemistry class follow a normal distribution with mean 72 and standard deviation 8. Question 39 (1 point) What proportion of students in the Chemistry class score between 62 and 76 marks? 0.7066 O 0.5859 0.6247 0.6842 O 0.5587

Answer 1

Solution :

Given that ,

Chemistry class

mean = $\mu$ = 72

standard deviation = $\sigma$ = 8

P( 62 < x < 76 )

= P[( 62 - 72 ) / 8) < (x - $\mu$ ) /$\sigma$  < ( 76 - 72) / 8) ]

= P( -1.25 < z < 0.5 )

= P(z < 0.5 ) - P(z < -1.25)

Using z table,

= 0.6915 - 0.1056

= 0.5859

Proportion = 0.5859

Correct option : - 0.5859

40.

math class

mean = $\mu$ = 60

standard deviation = $\sigma$ = 12

P( 62 < x < 76 )

= P[( 62 - 60) / 8 ) < (x - $\mu$ ) /$\sigma$  < ( 76 - 60) / 12 ) ]

= P( 0.25 < z < 2 )

= P(z < 2 ) - P(z < 0.25 )

Using z table,

= 0.9772 - 0.5987

= 0.3785

Proportion = 0.3785