Question

Let X be the exam grade of a student taking Calculus 1 with Professor Smith. The professor believes that X has a mean of 81 and a standard deviation of 22. Suppose there are 100 students in Professor Smith's class.

Approximate the probability that X is higher than 83.6 OR smaller than 79.2?

Answer 1

Solution :

Given that,

mean = = 81

standard deviation = = 22

n = 100

= 81

₌ / n = 22 100= 2.2

P ( > 83.6 )

= 1 - P ( < 83.6 )

= 1 - P ( - / ) < ( 83.6 - 81/ 2.2)

= 1 - P ( z <2.6 /2.2)

= 1 - P ( z < 1.18 )

Using z table

= 1 - 0.8810

= 0.1190

P( <79.2 )

P ( - /  ) < ( 79.2 - 81 / 2.2)

P ( z < -1.8 / 2.2 )

P ( z < -0.81)

= 0.1190 + 0.2090

= 0.3280

Probability = 0.3280