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The average weight of pine trees in a forest is normally distributed with mean 53.45 and
a standard deviation of 2.51. A sample of 20 pine trees are taken from the forest and their mean
is recorded 64.85. Test the hypothesis that the average weight is less than 2.51. Using Z 2.83 = .
Approximately 60% of all part-time college students in the Peshawar are female. What would
you expect to see in terms of the behavior of a sample proportion of females if random samples of
size 100 were taken from the population of all part-time college students? Estimate the standard
deviation also construct the confidence interval using alpha 0.05.
Q1 - Q9 Austin has 2.5k subscribers on his “First date 101” YouTube channel. In order to produce videos that his subscribers will enjoy, he randomly selected 50 subscribers and investigated whether their dating history (represented by how many people that the subscriber has dated previously) affects the time they spent on his channel.--------------------
Q9 Austin found out that people who dated fewer people spent more time on his channel. As a result, he claims that less dating history causes people to watch longer. What is the main problem of making this causal statement?
A. Temporal precedence is not aligned with the direction of the cause
B. Alternative explanations for the relationship have not been ruled out
C. The sample he selected is not representative
Cut fruit is packed for sale in a supermarket. The weights of packages are normally distributed with a mean of 201.49 grams and variance of 24.63 grams.
Given that 5% of the distribution lies below the Z value of -1.64485, find the package weight that has 5% of the distribution above it. Give your result correct to four decimal places.
A company has found that the proportion of claims made on travel insurance policies of up to 30 days to Europe is 0.2586. It examines a sample of 250 policies and tries to find the probability that the proportion of claims made for these policies is more than 0.25.
What Z value should it use to calculate this probability? Give your answer correct to four decimal places.
An insurance company knows that the average insured value of the house policies it holds is $253255 with a standard deviation of $40648. It takes a random sample of 289 policies to investigate if insurance is adequate in light of recent natural disasters and finds that the probability is 0.15 that the average insured value of this sample exceeds an amount A.
Using the Excel formula, calculate the value of A correct to the nearest cent.
A box contains 10,000 widgets. Pat tells you that 2% of the widgets in a box are made of copper and the
rest are made of steel. If you randomly select 15 widgets from the box, find the probability that less than 2 of the
widgets you select are made of copper.
A small airport is served by four airlines: A, B, C which offer overseas flights, and D which offers domestic flights.
Over a one month period, the number of on-time and delayed arrivals are recorded for all four airlines. They are shown in the table below.
What is the probability that a flight was delayed and it was run by airline D? Give your answer correct to four decimal places.
Airline On-Time Delayed
A 105 15
B 38 20
C 21 7
D 200 59
A company runs a corporate event which offers a total of three identical lucky door prizes of tablet computers. Each person who purchases a ticket and attends the event has an equal chance of winning and can only win one tablet.
If 991 people attend the event and three are chosen to win tablets, in how many ways can the tablets be distributed?
Give your answer to the nearest integer entering numbers only.
A contractor builds houses that include the 50% of the market. The average size of houses he builds is 80 square meters and the standard deviation is 10 square meters. Assume that the variable is normally distributed, what are the maximum and minimum sizes of houses he should build?
