A rubber tree is 95 inches tall and growing at a rate of 4 inches per year. A cactus is 40 inches tall and growing at arate of 5
1 answer:
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Answer:
(a) Between 27 and 31 pounds per month = 0.62465
(b) More than 30.2 pounds per month = 0.1357
Step-by-step explanation:
We are given that each month, an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard deviation is 2 pounds and the variable is approximately normally distributed.
<em>Let X = generation of newspaper for garbage or recycling</em>
The z-score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = population average = 28 pounds
= population standard deviation = 2 pounds
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
(a) Probability of household generating between 27 and 31 pounds per month is given by = P(27 pounds < X < 31 pounds) = P(X < 31 pounds) - P(X 27 pounds)
P(X < 31 pounds) = P( <
) = P(Z < 1.50) = 0.93319
P(X 27 pounds) = P(
) = P(Z
-0.50) = 1 - P(Z < 0.50)
= 1 - 0.69146 = 0.30854
<em>{Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.50 and x = 0.50 in the z table which has an area of 0.93319 and 0.30854 respectively.}</em>
Therefore, P(27 pounds < X < 31 pounds) = 0.93319 - 0.30854 = 0.62465
(b) Probability of household generating more than 30.2 pounds per month is given by = P(X > 30.2 pounds)
P(X > 30.2 pounds) = P( >
) = P(Z > 1.10) = 1 - P(Z
<em> </em>1.10)
= 1 - 0.8643 = 0.1357
<em>Now, in the z table the P(Z </em><em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.10 in the z table which has an area of 0.8643.</em>
Answer:
Step-by-step explanation:
Two cases arise to obtain the median.
Case (1): Sample size (n) is odd
First, arrange the data in ascending order. Then, the median is the middle value and lies at the position.
Case (2): Sample size (n) is even
First, arrange the data in ascending order. Then, the median is the mean of the two data values that lie on and positions.
Formula for mean is, where is the sum of all observations and n is the total number of observations.
(1)
Use the below process to create a set of 5 positive numbers (repeats allowed) that have median 7 and mean 10.
1.Select the 5 ordered numbers with middle value 7.
2.Adjust the remaining 4 numbers other than 7 to get mean 10 without changing the order of the numbers.
Based on the process to select the 5 ordered numbers with middle value 7 and change the other ordered numbers to get the mean value 10.
(2)
The product of the mean and the total number of observations is obtained. Then, the sum of four observations is subtracted from the product.
Here, the first four numbers are (5, 6, 7, 8).
The last number by using mean 10 is,
The last number is 24.