Problem#12 on Exam#3 review sheet: There is an 80% chance that it will rain on any given day in seattle. What is the probability that, of 118 randomly selected days there will be rain on at most 90 of them?
Step 1: We figure out what n, p, q, and x first. n= 118, p= .8, q= .2, x= 1 to 90
Step 2: We figure out if both np and nq is greater than 5. np= 94.4, nq= 23.6 and both np and nq are greater than 5 so we can use the normal distribution.
Step 3: We have to figure out what the µ is and what σ is. µ= 94.4 and σ= 4.345112196
Step 4: We now convert the x to z. Because it is “at most” we add .5 to our original x before then apply that number which it is 90.5 to the formula. z=-.8975602526 and we round it to the nearest tenth place so z=-.9.
Step 5: We look up the z in the chart and the probability is 0.1841