The Central Limit Theorem says that the sampling distribution of the mean is approximately normal under certain conditions.  Which of the following is one of the conditions?

Pyramid Lake is in Nevada. The lake is famous for cutthroat trout. It has been widely advertised that the average length of trout caught in Pyramid Lake isµ = 19 inches. In a recent sample, however, of a random sample of 65 fish caught from the lake, the mean length was 18.5 inches with a standard deviation of 3.2 inches. Can it beclaimed that the average length of a trout caught from Pyramid Lake is less than 19 inches? Use a significance level of α = 0.01.  1. Which of the following would be the correct null and alternative hypothesis for this problem?  [null] a. Ho:

The mean cost of a ticket to a concert is $65 with a standard deviation of $12.  Would it be unusual for a ticket to cost $40? [yes] it would [beunusual] because $40 [is] between [interval].  

A college instructor is teaching a summer class and believes that there is an association between the temperature and the number of students absent.  The instructor randomly chooses a sample of days and records the temperature, in degrees Fahrenheit, and the number of students absent.  Temp. oF (x) 72 85 91 90 88 98 75 100 80 Number Absent (y) 3 7 10 10 8 15 4 15 5 1. Find the linear correlation coefficient r for this data set.  Round to three decimal places. [r] 2. A hypothesis test is to be done to determine if there is linear correlation between temperature and number of students absent.  The null and alternative hypotheses are given below.  Use a 0.05 level of significance.          

Global warming is a major issue facing the world today.  Documenting the mean surface temperature of the earth over time is one measure of global warming.  The data below represents the mean surface temperature of the earth calculated every 10 years from 1930 – 2020.  The data below gives the number of years past 1900 (considered year 0) and the mean surface temperature of the earth in degrees Fahrenheit.  Year      Years past 1900(x) Mean Surface Temperature oF (y) 1930 30 57.1 1940 40 57.3 1950 50 56.9 1960 60 57.2 1970 70 57.3 1980 80 57.6 1990 90 57.8 2000 100 57.8 2010 110 58.3 2020 120 58.7 1. Find the linear correlation coefficient r for this data set.  Round to three decimal places. [r] 2. A hypothesis test is to be done to determine if there is linear correlation between years past 1900 and mean surface temperature.  The null and alternative hypotheses are given below.  Use a 0.05 level of significance.          

27% of SMC students plan to transfer to a CalState.  A random sample of 16 SMC students is chosen.  1) What is the probability that exactly 5 plan to transfer to a CalState?  [ans1] 2) What is the probability that less than 7 plan to transfer to a CalState?   [ans2]  

A law firm tracks the number of calls from new clients received per day.  They construct the probability distribution provided below.  number of calls (x) 1 2 3 4 5 6 7 P(x) 0.03 0.14 0.27 0.33 [P5] 0.04 0.02 1. Complete the table by finding P(5).   2. What is the expected number of calls per day at the firm? [exp] 3. What is the probability that the firm receives at least 3 calls on a given day?  [atleast]

The amounts spent for a one-day trip to Disneyland are bell-shaped with a mean of $171 per person and a standard deviation of $22 per person.  Use the Empirical Rule to answer the following questions.  1. What percentage of amounts are between $127 and $193?  [ans1] 2. 95% of amounts spent are between _______________.  [ans2]

A research firm is interested in estimating the mean time that it takes a letter mailed in California to arrive in New York.  A sample of 100 letters is mailed and it is found that the 95% confidence interval for the mean delivery time is 6.2 days to 8.3 days.  Use this information to answer the following questions.  1. What was the sample mean delivery time?  [samplemean] 2. What was the calculated error in the delivery time?  [error]    

The five number summary for the commute times, in minutes, of Santa Monica College students is provided below.  1. 5 2. 20 3.  35 4.  49 5. 121 Interpret the value of the third quartile in a contextualized sentence, using the method from class.  [per] of Santa Monica College Students spend [amnt] per day commuting.