Given:
- The Mean:
![\mu=19.9](https://img.qammunity.org/2023/formulas/mathematics/college/5mao29y5195g5tpvin82po0g9dwdea09cu.png)
- The Standard Deviation:
![\mu=33.1](https://img.qammunity.org/2023/formulas/mathematics/college/mwms9f8dqzijjnoojaoapsi7vbqq1j1iqr.png)
You have to find:
![P(x>8.9)](https://img.qammunity.org/2023/formulas/mathematics/college/uwde4yjctrkdt7787qv2sk5uujojeb2t4q.png)
You need to find the z-statistic using this formula:
![z=(x-\mu)/(\sigma)](https://img.qammunity.org/2023/formulas/mathematics/college/h06hsre30elxbqnbdkqzw5pbp57988qa0r.png)
In this case:
![x=8.9](https://img.qammunity.org/2023/formulas/mathematics/college/zzzu6ax9wbr3hxllxv05dldt4fwga42x2f.png)
Then:
![z=(8.9-19.9)/(33.1)\approx-0.332](https://img.qammunity.org/2023/formulas/mathematics/college/lezn7x8guks1pf7gb0r0aekdb5dvg2xf0n.png)
You need to find:
![P(z>-0.332)](https://img.qammunity.org/2023/formulas/mathematics/college/hkkk61ltpon981xws6y95oo4mvdv8cokjs.png)
By symmetry, this is equal to:
![P(z<0.0332)](https://img.qammunity.org/2023/formulas/mathematics/college/nlpck7okj8rpxjvof5obdyu77qbpaplzkn.png)
Using the Normal Distribution Table, you get:
![P(z<0.0332)=0.6293](https://img.qammunity.org/2023/formulas/mathematics/college/7fky9pi0gwu71707gs3asa9qk603nnrraw.png)
Hence, the answer is:
![P(x>8.9)=0.6293](https://img.qammunity.org/2023/formulas/mathematics/college/kizkm7n3yeswgo1bmpe5tozgd8b894x1t8.png)