This is a follow up question from the previous question that I have asked here. Can you draw an illustration through the bell shaped curve and highlight the area being asked. 1. The probability that a student has a score less than 24 is = ? P( X < 24 ) is, = P( [ X - µ ] / σ < [ 24 - 24.8 ] / 4.507 ) = P( z < -0.8 / 4.507 ) = P( z < -0.1775 ) Using the standard normal table or z table or excel Then P( z < -0.1775 ) is, = 0.4295 2. The probability that a student has a score greater than 30 is = ? P( X > 30 ) is, = 1 - P( X < 30 ) = 1 - P( [ X - µ ] / σ < [ 30 - 24.8 ] / 4.507 ) = 1 - P( z < 5.2 / 4.507 ) = 1 - P( z < 1.1537 ) Using the standard normal table or z table or excel = 1 - 0.8756 = 0.1244 3. The probability that a student has a score less than 15 or greater than 33 is = ? P( X < 15 ) or P( X > 33 ) is, = P( [ X - µ ] / σ < [ 15 - 24.8 ] / 4.507 ) + P( [ X - µ ] / σ < [ 33 - 24.8 ] / 4.507 ) = P( z < -2.1744 ) + P( z < 1.8194 ) Using the standard normal table or z table or excel = 0.0148 + 0.9655 = 0.9803
This is a follow up question from the previous question that I have asked here. Can you draw an illustration through the bell shaped curve and highlight the area being asked.
1.
The probability that a student has a score less than 24 is = ?
P( X < 24 ) is,
= P( [ X - µ ] / σ < [ 24 - 24.8 ] / 4.507 )
= P( z < -0.8 / 4.507 )
= P( z < -0.1775 )
Using the standard normal table or z table or excel
Then
P( z < -0.1775 ) is,
= 0.4295
2.
The probability that a student has a score greater than 30 is = ?
P( X > 30 ) is,
= 1 - P( X < 30 )
= 1 - P( [ X - µ ] / σ < [ 30 - 24.8 ] / 4.507 )
= 1 - P( z < 5.2 / 4.507 )
= 1 - P( z < 1.1537 )
Using the standard normal table or z table or excel
= 1 - 0.8756
= 0.1244
3.
The probability that a student has a score less than 15 or greater than 33 is = ?
P( X < 15 ) or P( X > 33 ) is,
= P( [ X - µ ] / σ < [ 15 - 24.8 ] / 4.507 ) + P( [ X - µ ] / σ < [ 33 - 24.8 ] / 4.507 )
= P( z < -2.1744 ) + P( z < 1.8194 )
Using the standard normal table or z table or excel
= 0.0148 + 0.9655
= 0.9803
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