On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 112 and a standard deviation of 17. Suppose one individual is randomly chosen. Let X = IQ of an individual. a. What is the distribution of X? X ~ N(. , ) b. Find the probability that a randomly selected person's IQ is over 124. Round your answer to 4 decimal places. c. A school offers special services for all children in the bottom 7% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places. d. Find the Inter Quartile Range (IQR) for IQ scores. Round your answers to 2 decimal places. Q1: Q3: IQR: Suppose that the weight of seedless watermelons is normally distributed with mean 6.8 kg. and standard deviation 1.8 kg. Let X be the weight of a randomly selected seedless watermelon. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N.(. , ) b. What is the median seedless watermelon weight? kg. c. What is the Z-score for a seedless watermelon weighing 7.7 kg? d. What is the probability that a randomly selected watermelon will weigh more than 7.5 kg? e. What is the probability that a randomly selected seedless watermelon will weigh between 6 and 6.5 kg? f. The 80th percentile for the weight of seedless watermelons is? kg.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
On a planet far far away from Earth, IQ of the ruling species is
a. What is the distribution of X? X ~ N(. , )
b. Find the
c. A school offers special services for all children in the bottom 7% for IQ scores. What is the highest IQ score a child can have and still receive special services? Round your answer to 2 decimal places.
d. Find the Inter
Q1:
Q3:
IQR:
Suppose that the weight of seedless watermelons is normally distributed with mean 6.8 kg. and standard deviation 1.8 kg. Let X be the weight of a randomly selected seedless watermelon. Round all answers to 4 decimal places where possible.
a. What is the distribution of X? X ~ N.(. , )
b. What is the
c. What is the Z-score for a seedless watermelon weighing 7.7 kg?
d. What is the probability that a randomly selected watermelon will weigh more than 7.5 kg?
e. What is the probability that a randomly selected seedless watermelon will weigh between 6 and 6.5 kg?
f. The 80th percentile for the weight of seedless watermelons is? kg.
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