Suppose that the IQ of adults is normally distributed with a mean of 100 and standard deviation of 15.

(a) What IQ score distinguishes the highest 10%?

(b) What is the probability that a randomly selected person has an IQ score between 91 and 118?

(c) Suppose people with IQ scores above 125 are eligible to join a high-IQ club. Show that approximately 4.78% of people have an IQ score high enough to be admitted to this particular club.

(d) Let X be the number of people in a random sample of 25 who have an IQ score high enough to join the high-IQ club. What probability distribution does X follow? Justify your answer.

(e) Using the probability distribution from part (d), find the probability that at least 2 people in the random sample of 25 have IQ scores high enough to join the high-IQ club. (f) [3 marks] Let L be the amount of time (in minutes) it takes a randomly selected applicant to complete an IQ test. Suppose L follows a uniform distribution from 30 to 60. What is the probability that the applicant will finish the test in less than 45 minutes?

There was an SRS of 100 flights on a large airline (airline 1) that showed that 64 of the flights were on time. An SRS of 100 flights of another large airline (airline 2) showed that 80 of the flights were on time. Let p₁ and p₂ be the proportion of all flights that are on time for these two airlines.

What is a 95% confidence interval for the difference p₁-p₂?

This is for thermodynamics:

"The latent heat of vaporization for water at 1 atm and 100 degrees C is 2.26x10³ kJ/kg. Calculate the latent heat for water at 2 atm and 100 C by combining the heat per kg required to turn liquid water into steam at 1 atm with the heat per kg required to change the pressure of that steam from 1 atm to 2 atm at a temperature of 100 C. Treat the steam as an ideal gas, and take the molar mass of water to be M = 18.015x10^-3 kg/mol."

The mean weight of an adult is 60 kilograms with a variance of 100

If 118 adults are randomly selected, what is the probability that the sample mean would be greater than 62.2 kilograms? Round your answer to four decimal places.

Fair Coin? In a series of 100 tosses of a token, the proportion of heads was found to be 0.61. However, the margin of error for the estimate on the proportion of heads in all tosses was too big. Suppose you want an estimate that is in error by no more than 0.03 at the 95% confidence level. (a) What is the minimum number of tosses required to obtain this type of accuracy? Use the prior sample proportion in your calculation. You should toss the token at least times. (b) What is the minimum number of tosses required to obtain this type of accuracy when you assume no prior knowledge of the sample proportion? You should toss the token at least times.

Fair Coin? In a series of 100 tosses of a token, the proportion of heads was found to be 0.61. However, the margin of error for the estimate on the proportion of heads in all tosses was too big. Suppose you want an estimate that is in error by no more than 0.04 at the 90% confidence level.

(a) What is the minimum number of tosses required to obtain this type of accuracy? Use the prior sample proportion in your calculation. You should toss the token at least ____ times.

(b) What is the minimum number of tosses required to obtain this type of accuracy when you assume no prior knowledge of the sample proportion? You should toss the token at least ____ times.

f there are 100 individuals in a population and 20 are homozygous for B, 60 are heterozygous, and 20 are homozygous for b, what is the allele frequency of B? 80 percent

Suppose that the IQ of adults is normally distributed with a mean of 100 and standard deviation of 15. not sure with current solution posted, personally it wasn't clear step by step working. I get lost with some values that he gets ( not sure where he gets them )

here's the question:

To get full marks for the following questions you need to convert the question from words to a mathematical expression (i.e. use mathematical notation), defining your random variables where necessary, and using correct probability statements.

Suppose that the IQ of adults is normally distributed with a mean of 100 and standard deviation of 15.

1. (a) [2 marks] What IQ score distinguishes the highest 10%?

2. (b) [3 marks] What is the probability that a randomly selected person has an IQ score between

   91 and 118?

3. (c) [2 marks] Suppose people with IQ scores above 125 are eligible to join a high-IQ club. Show that approximately 4.78% of people have an IQ score high enough to be admitted to this particular club.

4. (d) [4 marks] Let X be the number of people in a random sample of 25 who have an IQ score high enough to join the high-IQ club. What probability distribution does X follow? Justify your answer.

5. (e) [2 marks] Using the probability distribution from part (d), find the probability that at least 2 people in the random sample of 25 have IQ scores high enough to join the high-IQ club.

6. (f) [3 marks] Let L be the amount of time (in minutes) it takes a randomly selected applicant to complete an IQ test. Suppose L follows a uniform distribution from 30 to 60. What is the probability that the applicant will finish the test in less than 45 minutes?

The lengths (in mm) of a sample of 100 largemouth bass are given in the file LargemouthBass.csv in Digital appendices. (You can find this file under the “Digital Appendices” link on Blackboard.) Use R construct a frequency distribution table and histogram of these data.

A probability of 1 is the same as a probability of 100%

The difference between interval and ordinal data is that interval data has a natural zero.

If you are doing a study and the population is Americans, the easiest type of study to run would be a simple random sample.

If your population is 80% female and your sample is 60% male, there is undercoverage bias.

In order to calculate a mean on Excel, we type in "=MEAN".