statistics
Statistics Homework
50 points
1. Suppose IQ scores are normally distributed with mean 100 and standard Statistics Homeworkdeviation 16. If 36 people are randomly selected,
a. Find the mean and standard deviation of the sampling distribution of sample
mean (3 points)
b. What is the probability that the mean IQ score is less than 96. (3 points)
c. What is the probability that the mean IQ score is more than 102. (3 points)
d. What is the probability that the IQ score of a single person lies between 90 and 110 (3 points)
2. A college’s data about the incoming freshmen indicates that the mean of their high school GPAs is 3.6 with a standard deviation of 0.40. The distribution is normal. The students are randomly assigned to freshmen writing seminars in groups of 25.
a. Find the mean and standard deviation of the sampling distribution of sample
mean(3 points)
b. Find the probability that the average GPA is greater than 3.5. (3 points)
c. Find the probability that the average GPA is lower than 3.3. (3 points)
d. Find the probability that the GPA of a single student is between 3.1 and 3.6
(3 points)
3. In the 1980’s it was generally believed that autism affected about 8% of the nation’s children.. A recent study examined 400 children and found that 45 of them showed signs of some form of autism.
a. Find the 94% confidence interval for proportion of children having autism. (5 points)
b. Interpret the interval.(2 points)
4. . Research conducted a few years ago showed that 35% of UCLA students had travelled outside the US. A new survey showed that out of the100 randomly sampled students 42 have travelled abroad.
Find the “96% confidence interval” for the true mean proportion of
Students travelled abroad (5 points0
b. Interpret it.(2 points0
5. 42% of Jacksonville residents said that they had been in a hurricane. How many adults should be surveyed to estimate the true proportion of adults who have been in a hurricane( margin of error = 3% and confidence =98%) [6 points]
6. Using a 35% planned proportion estimate, find the sample size needed to achieve 6% margin of error for the female student survey at 96% confidence level. ( 6 points)