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

pakistan's principal natural resources are arable land and water. about 25% of pakistan's agriculture accounts for about 21% [1] of gdp and employs about 43% of the labour force. in pakistan, the most agricultural province is punjab where wheat and cotton are the most grown.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4