Question

The heights of players in Major League Baseball are normally distributed and have a minimum of 5.5 feet and maximum of 6.83 feet. Someone in our class explains that the standard deviation must be less than ¼ of the difference between the max and the min. To what extent do you agree? Totally agree, somewhat agree, disagree. Defend your decision by including a sketch of a normal curve and referring to properties of the normally distributed data discussed in this unit.   

Answer 1

Totally agree.

Because heights of players in Major League Baseball are normally distributed and normal distribution is symmetric about the mean.

Minimum=5.5 feet

Maximum =6.83 feet

So, we can take mean as average of minimum and maximum.

So, 99.22% of the data lies within 5.5 and 6.83 Which seems true for approximately normal distribution.

i.e. 99.22% of the data lies between minimum and maximum value.

If standard deviation is more than 0.25 then less than 99% data lies between minimum value and maximum value which is not true for approximately normal distribution.