Question

Bass: The bass in Clear Lake have weights that are normally distributed with a mean of 2.5 pounds and a standard deviation of 0.8 pounds.

Determine the weights that delineate the middle 90% of the bass in Clear Lake. Round your answers to 2 decimal places.

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Answer 1

Solution:-

Given that,

mean = = 2.5

standard deviation = = 0.8

Using standard normal table,

P( -z < Z < z) = 90%

= P(Z < z) - P(Z <-z ) = 0.90

= 2P(Z < z) - 1 = 0.90

= 2P(Z < z) = 1 + 0.90

= P(Z < z) = 1.90 / 2

= P(Z < z) = 0.95

= P(Z < 1.645) = 0.95

= z  ± 1.645

Using z-score formula,

x = z * +

x = -1.645 * 0.8 + 2.5

x = 1.18

Using z-score formula,

x = z * +

x = 1.645 * 0.8 + 2.5

x = 3.82

The middle 90% are from 1.18 pounds to 3.82 pounds