Question

a population of dolphins has weights that are normally distributed with u=80 and o=10

a sample of size n=36 is taken out at random. let x be the mean of the sample weights. find the following:

ux

ox

P (77<x<83)

P(x<78)

Answer 1

A population of dolphins has weights that are normally distributed with = 80 and = 10

A sample of size n = 36 is taken out at random.

Sample mean is given by,

and sample variance is given by,

= 0.2778

P(77 < X < 83)

= P(X< 83 ) - P(X< 77)

= 0.2358

P(X<78)

= 0.4207

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