Question

1. ) Suppose College male students’ heights are normally distributed with a mean of µ = 69.5 inches and a standard deviation of σ =2.8 inches.

1. What is the probability that randomly selected male is at least 70.5 inches tall?
2. If one male student is randomly selected, find the probability that his height is less than 65.2 inches or greater than 71.2 inches.
3. How tall is Shivam if only 30.5% of students are taller than him
4. There are 30.5% of all students between Mike’s height and 75 inches. How tall is Mike?
5. If 25 male students are randomly selected, find the probability that they have a mean height no higher than 70.2 inches.

Answer 1

Suppose College male students heights are normally distributed with a mean of = 69.5 inches & standadrd deviation of a = 2.8 inches.

a) -

Probability that randomly selected male is at least 70.5 inches tall -

  

  

Probability that randomly selected male is at least 70.5 inches tall is 0.3594.

b) -

Probability that his height is less than 65.2 iches or greater than 71.2 inches -

  

  

Hence, Probability that his height is less than 65.2 iches or greater than 71.2 inches = 0.2709 + 0.0618 = 0.3327

c) -

Height of shivam if only 30.5% of students are taller than him - P(X>x) = 0.305

Height of shivam is 70.928 inches.

d) -

There are 30.5% of all students between Mike's height & 75 inches, height of mike is -

height of mike is 70.732 inches.

e) -

If 25 students are seleced randomly, probability that they have a mean height no higher than 70.2 inches -

  

  

  

Probability that they have a mean height no higher than 70.2 inches is 0.8944.