Question

The average test marks in a particular class is 79. The standard deviation is 5. If the
marks are normally distributed, how many students in a class of 200 did not receive marks
between 75 and 82?​

Answer 1

Answer:

60

Step-by-step explanation:

Z is standard normal variant with mean and standard variation.

Z=(x-79)/5

For x=75.

z=(75–79)/5=-4/5=-8

For x=82,. Z=(82–79)5=3/5=.6

Now p(-.8<z<.6)=p(-.8<z<0)+p(0<z<.6)

=.2881+.2258. (table values)

=.5139 ……….p(-.8<z<0)=p(0<z<.8)

Probability of students not received marks between 75 and 82 is 1-.5139=.4861

Number of such students=.4861×124=60

Answer 2

Answer:

97

Step-by-step explanation:

Z is standard normal variant with mean and standard variation.

Z=(x-79)/5

For x=75.

z=(75–79)/5=-4/5=-8

For x=82,. Z=(82–79)5=3/5=.6

Now p(-.8<z<.6)=p(-.8<z<0)+p(0<z<.6)

=.2881+.2258. (table values)

=.5139 ……….p(-.8<z<0)=p(0<z<.8)

Probability of students not received marks between 75 and 82 is 1-.5139=.4861

Number of such students=.4861×200=97