Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.) 𝜇 = 6; 𝜎 = 2 P(5 ≤ x ≤ 8) =

Answer 1

2 standard deviations to the right

1 to the left

(jokers to the right, clowns to the left, as one golden oldie pop song lyrics read)

by the empirical rule 68-95-99.7, means (1-95)/2=5/2 = 2.5% to the right

(1-68)/2 = 32/2 = 16% to the left

total 18.5% outside

1-.185 = 81.5% as the answer

but for a far more exact answer, try z tables or an online z calculator or a hand calculator with statistics functions.

for better accuracy go for a z calculator.

but 81.5% is very roughly accurate.

You can call it 0.8150 = 81.50 % for 4 decimal places, but the empirical rule rounds off to an integer at best.

BUT using z tables

leaving 0.1587 +.0228 + .1815 = 18.15%

P(5<x<8) = 1-.1815 = 100% - 18.15% = 80.85%

P(5<x<8) = 80.85%