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The mean score and standard deviation in the Statistics test are respectively equal to 80 and 2.5, whereas in the Mathematics test the mean score is 70 and the standard deviation is 2. If Liza got a score of 85 in Statistics and a score or 75 in Mathematics in which subject is her standing better assuming normality in both subjects?
The results of a nationwide aptitude test in mathematics are normally distributed with the mean=63 and standard deviation=5. What is the 97.5th percentile?
1. What are the critical values of for area in two tails when the sample size is 29 with confidence level of 98%?
2. Find the area to the left of critical
value = 2.500 when the sample size is 29. [Hint: One-tailed test]
A random sample of 81 deaths in a certain area during the past year showed an average life span of 71.8 years. Assuming that the population standard deviation is 8.9, does this seem to indicate that the average life span today is significantly greater than 70 years old? Use a 0.05 level of significance.
participants is decreased by an average of 15%. A random sample of 25 graduates of this
course found an average 14.14 % the sample standard deviation was 3.61%. Test the clinic’s
claim at 5% level of significance.
Determine the critical value of the problem. Show your Solution.
A researcher claims that 75% of college students would rather
spend their extra money for mobile phone loads than cigarettes.
Another researcher would like to verify this claim. She randomly
selected 400 college students. Two hundred ninety-six of these 400
student said that they would rather spend their extra money on mobile
phone loads than cigarettes. At 0.05 level of confidence, is there
enough evidence to conclude that the percentage of students who
would rather spend their extra money for mobile phone loads than
cigarettes is different from 75%?
Note: H0 = p=p0
H0 = p=.75
H1 = p ≠ .75
Solution:
Answer:
. George estimates that there is a 30% chance of rain the next day if he waters the lawn, a 40% chance if he washes the car, and a 50% chance if he plans a trip to the beach. Assuming George’s estimates are accurate, what are the odds a) in favour of rain tomorrow if he waters the lawn? b) in favour of rain tomorrow if he washes the car? c) against rain tomorrow if he plans a trip to the beach?
A bag of marbles contains 12 red marbles and 16 green marbles. Two marbles are drawn.
What is the probability that:
a) Both marbles are green if the first marble is replaced? (A:2)
b) Both marbles are red if the first marble is not replaced? (A:2)
In a certain city, the daily consumption of water (in millions of litres) is a random variable with probability density function given by:
𝟏 𝒆−𝒙 𝒇(𝒙)={𝟗𝟗 , 𝒙≥𝟎
𝟎
(i) Identify the distribution and use its parameter to find the city’s expected water consumption for any given day. [3 marks]
(ii) What is the probability that the water supply on a given day is inadequate if the daily capacity of the city is 9 million litres?
These bags have a mean weight of 10kg with a standard deviation of 2kg.
a) Give the point estimate for the mean weight of all bags of cement in the warehouse. [ 1 marks ]
b) Compute the standard error. [1 marks ]
c) Construct the confidence interval of the mean weight of all the bags of cement in the warehouse
using 90% confidence level. [ 4 marks ]
d) If the inspector needs to estimate the mean weight of the bags with a maximum error of 0.5kg at the 90% confidence level, how large a sample will he need to take
