Suppose that it is known that the heights of male Shar Pei dogs are normally distributed...

Suppose that it is known that the heights of male Shar Pei dogs are normally distributed with a mean of 19.5 inches and a standard deviation of 0.5 inches. What proportion of male Shar Pei’s are between 19 and 21 inches? Round your answer to 3 decimal places.

Expert Solution

Here, μ = 19.5, σ = 0.5, x1 = 19 and x2 = 21. We need to compute P(19<= X <= 21). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (19 - 19.5)/0.5 = -1
z2 = (21 - 19.5)/0.5 = 3

Therefore, we get
P(19 <= X <= 21) = P((21 - 19.5)/0.5) <= z <= (21 - 19.5)/0.5)
= P(-1 <= z <= 3) = P(z <= 3) - P(z <= -1)
= 0.9987 - 0.1587
= 0.840

For P(z <= 3) z value is calculated as:

P(z <= -1) z value is calculated from the table as:

orchestra answered 1 year ago

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