Question

The heights of bigfoots are normally distributed with a mean of 250 cm and a standard deviation of 4 cm.

a) What is the probability that a bigfoot is taller than 258 cm?

b) What is the probability that a bigfoot is less than 246 cm tall?

c) What is the probability that a bigfoot is between 246 cm and 254 cm tall?

Answer 1

ANSWER:

Given that,

The heights of bigfoots are normally distributed with a mean of 250 cm and a standard deviation of 4 cm.

Mean = = 250 cm

Standard deviation = = 4 cm

a) What is the probability that a bigfoot is taller than 258 cm?

P(x > 258) = P(x- / > 258-250 /4 )

P(x > 258) = P(z > 8 /4 )

P(x > 258) = P(z > 2 )

P(x > 258) =1- P(z <2 )

P(x > 258) =1- 0.97725

P(x > 258) = 0.02275

b) What is the probability that a bigfoot is less than 246 cm tall?

P(x < 246) = P(x- / < 246-250 /4 )

P(x < 246) = P(z < 246-250 /4 )

P(x < 246) = P(z < -4 /4 )

P(x < 246) = P(z < -1)

P(x < 246) = 0.15866

c) What is the probability that a bigfoot is between 246 cm and 254 cm tall?

P(246 < x < 254) = P(246-250 /4 < x- / < 254-250 /4 )

P(246 < x < 254) = P(-4 /4 < z < 4/4 )

P(246 < x < 254) = P(-1 < z < 1 )

P(246 < x < 254) = P(z < 1 ) - P(z < -1)

P(246 < x < 254) = 0.84134 - 0.15866

P(246 < x < 254) = 0.68268

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