Weights of Newborn Hippos The weight of newborn hippopotami is approximately Normal, with a mean of 88 pounds and a standard deviation of 10 pounds. a. What is the probability that a newborn hippo weighs between 90 and 110 pounds? b. Suppose baby hippos that weigh at the 5th percentile or less at birth are unlikely to survive. What weight corresponds with the 5th percentile for newborn hippos? c. Fiona the Hippo was born at the Cincinnati Zoo in 2017, 6 weeks premature, and weighed only 29 pounds at birth. What percentage of baby hippos are born weighing 29 pounds or less?
Weights of Newborn Hippos The weight of newborn hippopotami is approximately Normal, with a mean of 88 pounds and a standard deviation of 10 pounds. a. What is the probability that a newborn hippo weighs between 90 and 110 pounds? b. Suppose baby hippos that weigh at the 5th percentile or less at birth are unlikely to survive. What weight corresponds with the 5th percentile for newborn hippos? c. Fiona the Hippo was born at the Cincinnati Zoo in 2017, 6 weeks premature, and weighed only 29 pounds at birth. What percentage of baby hippos are born weighing 29 pounds or less?
Weights of Newborn Hippos The weight of newborn hippopotami is approximately Normal, with a mean of 88 pounds and a standard deviation of 10 pounds.
a. What is the probability that a newborn hippo weighs between 90 and 110 pounds?
b. Suppose baby hippos that weigh at the 5th percentile or less at birth are unlikely to survive. What weight corresponds with the 5th percentile for newborn hippos?
c. Fiona the Hippo was born at the Cincinnati Zoo in 2017, 6 weeks premature, and weighed only 29 pounds at birth. What percentage of baby hippos are born weighing 29 pounds or less?
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
Question 3
The following stem-and-leaf displays the weekly salary of employees at this firm.
Stem-and-Leaf Display
Leaf Unit = 10.0
N=x
5
3 00123
12 4 0125888
(y)
5 11234456777
z
6 13568
5
7 154
2
8 46
i.
Determine the value of x, y and z.
[3]
ii. What is the value of the median?
[2]
iii.
Find the mode of this data set.
iv.
Calculate the range
[1]
[2]
Let Y be a continuous RV with PDF
otherwise
Find the CDF, Fry), of Y .
Find an expression for pth, p € (0, 1), quantile of the distribution.
Find E(Y) and V(Y).
Find E(-2Y + 1) and V(-3Y - 2).
Find E(Y3).
Let X be a continuous RV with CDF
Find P(X < 0), P(-1 < X < 1) and P(0.5 < X).
Based on your answers to the above questions, what is the median of the distribu-tion? Why
Find the PDF, fx (x), of X.
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