Suppose a geyser has a mean time between eruptions of 76 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 27 minutes. (round everything to four decimal places)

a) What is the probability that a randomly selected time interval between eruptions is longer than 87 minutes?

b) What is the probability that a random sample of 14 time intervals between eruptions has a mean longer than 87 minutes?

c) What is the probability that a random sample of 26 time intervals between eruptions has a mean longer than 87 minutes?

d) What effect does increasing the sample size have on the probability? Fill in the blanks with either increases or decreases.

If the population mean is less than 87 minutes, then the probability that the sample mean of the time between eruptions is greater than 87 minutes because the variability in the sample mean as the sample size .

e) What might you conclude if a random sample of 26 time intervals between eruptions has a mean longer than 87 minutes? Choose the best answer.

A) The population mean must be more than 76, since the probability is so low.

B) The population mean is 76, and this is an example of a typical sampling result.

C) The population mean must be less than 76, since the probability is so low.

D) The population mean may be greater than 76.

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9

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