Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

Question

Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Enter a number. Round your answer to four decimal places.)

𝜇 = 22; 𝜎 = 3.8

P(x ≥ 30) = 

Answer 1

Pictorially, you are looking for the little bit of the area under the normal curve for x > 30 (shaded in blue) like this:

The area under the curve is actually the probability you are looking for.

Using a TI-84, select the "distr" button. The button is actually got "vars" on it (it's 3 buttons up from the "9") but to get "distr", push the blue "2nd" button, then the "vars". Scroll down to "2: normalcdf(" and hit "enter". For "lower" enter "30". This is your lower limit where you want to start finding the area. For "upper" you want to enter a really big number - you can use 1 million (1000000). This is the upper limit where you want to stop finding the area. In all actuality, this should be infinity but it will work just fine with any large number. Then for "μ", type in "22" and for "σ", type in "3.8". The scroll down to highlight "Paste" and hit "enter, then hit "enter" a 2nd time.

The answer I got is 0.017634141 which rounded to 4 decimal places is 0.0176