Question

Andrea and Ashley are middle distance runner's for the schools traffic and FaceTime in the 500 m race are approximately normally distributed with a mean of 62 seconds in a standard of deviation of 0.8 seconds. The school record for the 400m is 60 seconds what is the probability the end of your breaks the record in her next race,

Answer 1

Answer:

0.006 is the probability that the record will be broken in next year.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 62 seconds

Standard Deviation, σ = 0.8 seconds

We are given that the distribution of face time is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

The record will be broken if the time is less than 60 seconds.

P(time is less than 60 seconds)

P(x < 60)

$P( x < 60) = P( z < \displaystyle\frac{60 - 62}{0.8}) = P(z < -2.5)$

Calculation the value from standard normal z table, we have,  

$P(x < 60) =0.006 = 0.6\%$

Thus, 0.006 is the probability that the record will be broken in next year.