Question

Sketch a normal distribution with µ = 80 and σ = 10. What is the probability of randomly selecting a score greater than 100 from this distribution?

Answer 1

Answer:

The sketch is provided in attached file.

0.0228

Step-by-step explanation:

The sketch is made by taking center at µ=80 and the desired probability of the mentioned area is also demonstrates.

The probability randomly selecting a score greater than 100 from this distribution can be calculated as

P(X>100)=P((X-µ)/σ > (100-80)/10)

P(X>100)=P(z>2)

P(X>100)=P(0<z<∞)-P(0<z<2)

Using normal table the probability corresponds to z-score=2 is 0.0228 and the area on the right side of normal curve is 0.5. So,

P(X>100)=0.5-0.4772=0.0228

The probability randomly selecting a score greater than 100 is 2.28%.