9 is greater than w, and 5 is less than or equal to w
2 answers:
You might be interested in
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 = <u><em>the interval of time between the eruptions</em></u>
So, X ~ N()
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = population mean time = 72 minutes
= 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( >
) = P(Z > 0.43) = 1 - P(Z
0.43)
= 1 - 0.6664 = <u>0.3336</u>
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 = <u><em>sample mean time between the eruptions</em></u>
The z-score probability distribution for the sample mean is given by;
Z = ~ N(0,1)
where, = population mean time = 72 minutes
= 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( > 82 min)
P( > 82 min) = P(
>
) = P(Z > 1.57) = 1 - P(Z
1.57)
= 1 - 0.9418 = <u>0.0582</u>
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 = <u><em>sample mean time between the eruptions</em></u>
The z-score probability distribution for the sample mean is given by;
Z = ~ N(0,1)
where, = population mean time = 72 minutes
= 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( > 82 min)
P( > 82 min) = P(
>
) = P(Z > 2.54) = 1 - P(Z
2.54)
= 1 - 0.9945 = <u>0.0055</u>
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.
Answer:
The linear regression model is .
Step-by-step explanation:
The given data points are (-6 4) (-4 0) (-3 -2) (-1 -7). Plot these points on a coordinate plane.
From the graph it is clear that the point are in the form of a straight line, so we need to use the linear regression model.
The general linear regression model is
Using technology we get
Put a=-2.19 and b=-8.92 in the above equation.
Therefore the linear regression model is .