Question

Two sprinters, Victor and Aaron, want to find out who has the faster time when compared to each of their teams. Victor has a time of 10.9 seconds, and his team has a mean time of 11.4 seconds and a standard deviation of 0.2 seconds. Aaron has a time of 10.6 seconds, and his team has a mean of 11.5 seconds and a standard deviation of 0.1 seconds. Who has the faster time when compared to each of their teams

Answer 1

The times are equal when compared to each of their teams.

Explanation:

Answer 2

The answer is "-9".

Explanation:

`\mu = 11.4\\\\\sigma = 0.2\\\\ x = 10.9\\\\`

`P(X <= 10.9)=?`

The z-value is determined using the central boundary theorem

`z = ((x - \mu))/(\sigma)`

`= ((10.9 - 11.4))/(0.2)\\\\ = -2.5`

Calculating the value for Aaron

`\mu = 11.5\\\\ \sigma = 0.1\\\\ x = 10.6\\\\ P(X <= 10.6)=?`

When the z-value is calculated using Central Limit Theorem

`z = ((x - \mu))/(\sigma)`

`= ((10.6 - 11.5))/(0.1)\\\\ = -9`