A study is done in Sydney to estimate the proportion of people living there who have travelled outside of Australia. Previous research has found that this proportion is equal to roughly 28%. a. Find the minimum sample size needed for the study in order to obtain a minimum of 5% margin of error in an approximate 95% confidence interval for this proportion. (use k=1.96)
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Can u plz solve the 9 questions given in the pictures below.!!!!!!!!
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The yield of a variety of Farmer Jase's pumpkin patch has a probability density function:
kx, 0 Sx<3
f(x) = }k(6 – x), 3 <x56
0.x<0 or x > 6
a. Find the variance
b. Find the probability Pr(u – 1<x < µ + 1)
c. Find the value of a such that Pr(X > a) = 0.6, giving your answer correct to one decimal place.
Example 6
In a small factory producing bamboo products, the standard acceptable measurement for a bamboo straws'
lengths are between 10.085 cm and 12.075 cm. Alexis has noticed that 6% of the straws are rejected for being
too short and another 6% are rejected for being too tall. What is the mean and standard deviation of
distribution assuming that the straws' lengths are normally distributed? (2dp)
Example 7
A sample of four chocolate bars are randomly selected from a box of ten. Six of the chocolates in the box are
milk chocolate. (without replacement)
a. Create a probability distrībution table showing the sampling distribution of the sample proportion
of milk chocolate bars in the sample.
b. Evaluate Pr(0<P< 0.7) and hence evaluate Pr(P < 0.7|P>0).
Example 8
In a particular university, the probability that any one student is male is 0.65. Four students are selected at
random from this university as a sample.
a. Create a probability distrībution table showing the sampling distribution of the sample proportion
of female students in the sample. (4dp)
b. Find Pr(P <0.65| P >0). (4dp)
Example 9
A study is done in Sydney to estimate the proportion of people living there who have travelled outside of
Australia. Previous research has found that this proportion is equal to roughly 28%.
a. Find the minimum sample size needed for the study in order to obtain a minimum of 5% margin of
error in an approximate 95% confidence interval for this proportion. (use k=1.96)
7:34 AM
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Hi
321
10/13/2020
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![D SIMPLE_SAMPLE_QUESTIONS_20 X
A CALCULUS_pdf.pdf
O File | C:/Users/USER/AppData/Local/Microsoft/Windows/INetCache/IE/68NCA10W/SIMPLE_SAMPLE_QUESTIONS_2020[1].pdf
A) Read aloud
V Draw
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Example 1
Does y = e9-x* - 2 exist? What is the domain & range of the function if it does exist? (show full working out)
Example 2
Sketch a graph for y = 2 sin (x +) + 1, x € [0,4x] (show full working out for all intercepts and turning
points).
Example 3
Find the derivative of In(3t² – 2t + 1) and then calculate f +3 dt (use integration by recognition).
Example 4
The probability of winning a prize in a game of chance is 0.48. What is the least number of games that must be
played to ensure that the probability of winning at least twice is more than 0.95?
Example 5
The yield of a variety of Farmer Jase's pumpkin patch has a probability density function:
kx, 0 Sx<3
f(x) = }k(6 – x), 3 S x56
0, x<0 or x> 6
a. Find the variance
b. Find the probability Pr(u – 1<X<µ+1)
c. Find the value of a such that Pr(X > a) = 0.6, giving your answer correct to one decimal place.
Example 6
In a small factory producing bamboo products, the standard acceptable measurement for a bamboo straws'
lengths are between 10.085 cm and 12.075 cm. Alexis has noticed that 6% of the straws are rejected for being
too short and another 6% are rejected for being too tall. What is the mean and standard deviation of
distribution assuming that the straws' lengths are normally distributed? (2dp)
Example 7
A sample of four chocolate bars are randomly selected from a box of ten. Six of the chocolates in the box are
milk chocolate. (without replacement)
a. Create a probability distribution table showing the sampling distrībution of the sample proportion
of milk chocolate bars in the sample.
b. Evaluate Pr(0<P< 0.7) and hence evaluate Pr(P<0.7|P>0).
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Hi
321
14
10/13/2020
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