Question

Ralph’s bowling scores in a single game are normally distributed with a mean of 120 and a standard deviation of 10.

Lucky Lolly’s bowling scores in a single game a normally distributed with a mean of 100 and standard deviation of 15.

1. Is Lolly or Ralph more likely to score over 165 in a single game? Show your work.
2. Is Lolly or Ralph more likely to score over 130 in a single game? Show your work.

Answer 1

Solution:

For Ralph , = 120 and = 10

For Lolly , = 100 and = 15

1)

For Ralph ,

P(X > 165)

= P[(X - )/ >  (165 - )/]

= P[Z > (165 - 120)/10]

=  P[Z > 4.50]

= 1 - P[Z < 4.50]

= 1 - 1 ( use z table)

= 0.0000

For Lolly ,

P(X > 165)

= P[(X - )/ >  (165- )/]

= P[Z > (165 - 100)/15]

=  P[Z > 4.33]

= 1 - P[Z < 4.33]

= 1 - 1 ( use z table)

= 0.0000

Both are same likely

2)

For Ralph ,

P(X > 130)

= P[(X - )/ >  (130 - )/]

= P[Z > (130 - 120)/10]

=  P[Z > 1.00]

= 1 - P[Z < 1.00]

= 1 - 0.8413 ( use z table)

= 0.1587

For Lolly ,

P(X > 130)

= P[(X - )/ >  (130- )/]

= P[Z > (130 - 100)/15]

=  P[Z > 2.00]

= 1 - P[Z < 2.00]

= 1 - 0.9772  ( use z table)

= 0.0228

Ralph is more likely