Question

Q5- (5marks) K is normally distributed with a mean of 80 and a 6) The weigh of students in AURA standard deviation of 7. If one students is selcted randomly a- What is the probability of student wight is more than 90 b- What is the probabilit of student wight is between 73 and 87

Answer 1

Consider x = The weight of student in AURAK

$x\sim N(\mu =80,\sigma =7)$

a) Probability of student weight is more than 90

P[x>90]

$=P[z>\frac{90-80}{7}]$

=P[Z>1.43]

$=1-P[z\leq 1.43]$

=1-0.9236...........................by using normal probability table.

=0.0764

b) The probability of student weight is between 73 and 87

$=P\left [ \frac{73-80}{7}<z<\frac{87-80}{7} \right ]$

=P[-1<z<1]

$=P[z\leq 1]-P[z\leq -1]$

=0.8413-0.1587.....................by using normal probability table.

=0.6826