The density function for the number of times the riders scream on a roller coaster is given by....

Suppose a geyser has a mean time between eruptions of 72 minutes. Let the interval of time between the eruptions be normally dis

nikitadnepr [17]

Answer:

(a) The probability that a randomly selected time interval between eruptions is longer than 82 minutes is 0.3336.

(b) The probability that a random sample of 13-time intervals between eruptions has a mean longer than 82 minutes is 0.0582.

(c) The probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes is 0.0055.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) The population mean must be more than 72, since the probability is so low.

Step-by-step explanation:

We are given that a geyser has a mean time between eruptions of 72 minutes.

Also, the interval of time between the eruptions be normally distributed with a standard deviation of 23 minutes.

(a) Let X = the interval of time between the eruptions

So, X ~ N( $\mu=72, \sigma^{2} =23^{2}$ )

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population mean time = 72 minutes

$\sigma$ = standard deviation = 23 minutes

Now, the probability that a randomly selected time interval between eruptions is longer than 82 minutes is given by = P(X > 82 min)

P(X > 82 min) = P( $\frac{X-\mu}{\sigma}$ > $\frac{82-72}{23}$ ) = P(Z > 0.43) = 1 - P(Z $\leq$ 0.43)

= 1 - 0.6664 = 0.3336

The above probability is calculated by looking at the value of x = 0.43 in the z table which has an area of 0.6664.

(b) Let $\bar X$ = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean time = 72 minutes

$\sigma$ = standard deviation = 23 minutes

n = sample of time intervals = 13

Now, the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 minutes is given by = P( $\bar X$ > 82 min)

P( $\bar X$ > 82 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{82-72}{\frac{23}{\sqrt{13} } }$ ) = P(Z > 1.57) = 1 - P(Z $\leq$ 1.57)

= 1 - 0.9418 = 0.0582

The above probability is calculated by looking at the value of x = 1.57 in the z table which has an area of 0.9418.

(c) Let $\bar X$ = sample mean time between the eruptions

The z-score probability distribution for the sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean time = 72 minutes

$\sigma$ = standard deviation = 23 minutes

n = sample of time intervals = 34

Now, the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes is given by = P( $\bar X$ > 82 min)

P( $\bar X$ > 82 min) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{82-72}{\frac{23}{\sqrt{34} } }$ ) = P(Z > 2.54) = 1 - P(Z $\leq$ 2.54)

= 1 - 0.9945 = 0.0055

The above probability is calculated by looking at the value of x = 2.54 in the z table which has an area of 0.9945.

(d) Due to an increase in the sample size, the probability that the sample mean of the time between eruptions is greater than 82 minutes decreases because the variability in the sample mean decreases as the sample size increases.

(e) If a random sample of 34-time intervals between eruptions has a mean longer than 82 minutes, then we conclude that the population mean must be more than 72, since the probability is so low.

6 0

3 years ago

Find the intersection points of the linear and quadratic functions shown below f(x)=2x-5 g(x)= x2+2x-21

Mice21 [21]

Answer:

$(-4,-13)$ and $(4,3)$ the intersection points.

Step-by-step explanation:

Intersection point of two functions is a common point which satisfies both the functions.

Given functions are,

$f(x)=2x-5$

$g(x)=x^2+2x-21$

For a common point of these functions,

$f(x)=g(x)$

$2x-5=x^2+2x-21$

$-5=x^2-21$

$0=x^2-16$

$x^2=16$

$x=-4,4$

For $x=-4$ ,

$f(-4)=g(-4)=2(-4)-5$

$=-13$

For $x=4$ ,

$f(4)=g(4)=2(4)-5$

$=3$

Therefore, $(-4,-13)$ and $(4,3)$ the intersection points.

3 0

3 years ago

Find the measure of angle ABD if the measure of angle DBC is 42 degrees and the measure of angle ABC is 88 degrees

snow_lady [41]

First, realize that angle ABC is the sum of the two other angles. Hence, form an equation in which you subtract the measure of one of the angles from angle ABC to get the measure of the other angle -- the one you are solving for.

6 0

3 years ago

Find the length of line segment GF.

amm1812

Pythagorean theorem
c2 = a2 + b2
71^2 = 43^2 + b2
5041 = 1849 + b2
3192 = b2
b = 56.5 which is answer choice d

8 0

3 years ago

(x-5)1/2+5=2 (x-5)1/2=-3 [(x-5)^1/2]^2=(-3)^2

Studentka2010 [4]

Answer:

x = 14

Step-by-step explanation:

You want to solve for x, right?

(x-5)^(1/2)+5=2

You have it right so far.

(x - 5)^(1/2) = -3

(x - 5) = (-3)^2

x - 5 = 9

x = 9 + 5 = 14

3 0

3 years ago