Question

The distribution of batting averages for players in the National League is approximately normal with a mean of 0.262 and a standard deviation of 0.039.

a. Find the probability (give 3 decimal places) that a player
has a batting average of 0.300 or higher? **Show all work
and steps.**

b. Only 25% of players have batting averages above what value?
Give 3 decimal places. **Show all work and
steps.**

Answer #1

let us consider x is the batting averages for players in the National League which is normally distributed with

mean () = 0.262

and variance () = 0.039

a) P(x = = P( = 0.1649

the probability that a player has a batting average of 0.300 or higher is 0.165

b ) from the z table value corresponding to 0.25 is .5987 so

x = = 0.262 + .5987 * 0.039

x = 0.285

Only 25% of players have batting averages above 0.285

In 2004, professional baseball players in the National League
had a mean batting average of 0.260 for the year with a standard
deviation of 0.040.
(a) What percentage of batters had an average above 0.300?
(b) What percentage of batters had an average between 0.100 and
0.200?
(c) What percentage of batters had an average between 0.200 and
0.300? Use the normal error curve table to do your calculations
Explain briefly plz!!!!

Suppose that the batting averages in a specific baseball league
are normally distributed with mean 250 and standard deviation 25.
If the league has 600 players, how many players would you expect to
have a batting average above 310?
Answer: 4.92 or 5. I just need to know how to get to this
answer, preferably by a calculator method! I have a TI-84 plus.
Thanks in advance.

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