Find the probability that x is between five and nine. (Round your answer to four decimal places.) X ~ N(6, 2)

0.62465

Step-by-step explanation:

Given that:

X ~ N(6, 2)

Distribution ia approximately Normal

Mean (m) of distribution = 6

Standard deviation (σ) = 2

Using the z formula :

Zscore = (x - mean) / standard deviation

X = 5

Zscore = (5 - 6) / 2

Zscore = - 1 / 2 = - 0.5

P(z < - 0.5) = 0.30854

x = 9

Zscore = (9 - 6) /2

Zscore = 3/2 = 1.5

P(z < 1.5) = 0.93319

Hence,

0.93319 - 0.30854 = 0.62465

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