Question
Asked Oct 13, 2019
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SAT Math scores have a bell-shaped distribution with a mean of 515 and a standard deviation of 114. 

a) What percentage of SAT scores is between 401 and 629

b) What percentage of SAT score is less than 401 or greater than 629?

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Expert Answer

Step 1

a.

 

The percentage of SAT scores is between 401 and 629 is 0.6826 and it is calculated below:

 

From the given information, let us define the rand...

P(401 Xs629) P(X< 629)-P(X< 401)
401-515
629-515
= P zS
- PzS
_
114
114
=P(z 1)-P(z-1)
From standard normal table,
P(z <-1)0.1587
0.8413-0.1587
P(z1)=0.8413
0.6826
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P(401 Xs629) P(X< 629)-P(X< 401) 401-515 629-515 = P zS - PzS _ 114 114 =P(z 1)-P(z-1) From standard normal table, P(z <-1)0.1587 0.8413-0.1587 P(z1)=0.8413 0.6826

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