The weights of male players in a basketball competition are approximately normally distributed with a mean of 78.6 kg and a standard deviation of 9.3 kg.
Part 1
There are 456 male players in the competition.
The expected number of male players in the competition with weights above 60 kg is closest to
- `3`
- `11`
- `23`
- `433`
- `445`
Part 2
Brett and Sanjeeva both play in the basketball competition.
When the weights of all players in the competition are considered, Brett has a standardised weight of `z` = – 0.96 and Sanjeeva has a standardised weight of `z` = – 0.26
Which one of the following statements is not true?
- Brett and Sanjeeva are both below the mean weight for players in the basketball competition.
- Sanjeeva weighs more than Brett.
- If Sanjeeva increases his weight by 2 kg, he would be above the mean weight for players in the basketball competition.
- Brett weighs more than 68 kg.
- More than 50% of the players in the basketball competition weigh more than Sanjeeva
`text(Part 1)`
`text(Find)\ ztext(-score of 60 kg)`
| `ztext(-score)` | `= (x – barx)/s` |
| `= (60 – 78.6)/9.3` | |
| `= −2` |
`text(Players with weight above 60 kg)`
`= 97.5text(%) xx 456`
`= 445`
`=> E`
`text(Part 2)`
`text(Calculate the weight of each player:)`
`text(Brett)`
| `−0.96` | `= (x – 78.6)/9.3` |
| `x` | `= (9.3 xx −0.96) + 78.6` |
| `~~ 69.7\ text(kg)` |
`text(Sanjeev)`
| `−0.26` | `= (x – 78.6)/9.3` |
| `x` | `= (9.3 xx −0.26) + 78.6` |
| `~~ 76.2\ text(kg)` |
`text(Consider)\ C,`
`76.182 + 2 = 78.182 < 78.6`
`:. C\ text(is not true.)`
`=> C`
