The table below gives the typical number of days of rainfall in Spring and Fall in Death Valley, California.

Spring (Event S)

Fall (Event F)

Rain (Event R) 7 6
No Rain or Dry (Event D) 115 116

On average, what is the approximate percent chance of rainfall on a given day in Spring or Fall in Death Valley.
Show your work.

5.3% is the answer i believe

13 divided by the total number of days (246) which you get by adding 7,6,115 and 116 together = 0.52something which rounds to 5.3

Step-by-step explanation:

f is the midpoint of

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.