The annual 2-mile fun-run is a traditional fund-raising event to support local arts and sciences activities. it is known that the mean and the standard deviation of finish times for this event are respectively \mu μ = 30 and \sigma σ = 5.5 minutes. suppose the distribution of finish times is approximately bell-shaped and symmetric. find the approximate proportion of runners who finish in under 19 minutes.

0.0228

Step-by-step explanation:

Given : The  mean and the standard deviation of finish times (in minutes) for this event are respectively as :-

If the distribution of finish times is approximately bell-shaped and symmetric, then it must be normally distributed.

Let X be the random variable that represents the finish times for this event.

z score :

Now, the probability of runners who finish in under 19 minutes by using standard normal distribution table :-

Hence, the approximate proportion of runners who finish in under 19 minutes = 0.0228

= 5

step-by-step explanation:

to find the 15th term substitute n = 15 into the nth term formula

= (- 3 × 15 ) + 50 = - 45 + 50 = 5