Stats Unit 2

Stats Unit 2.3 Which of these statements about the shape of a normally distributed data set is TRUE?  a.) The shape of the normal curve is controlled by the standard deviation of the data.  b.) The shape of the normal curve is controlled by the median of the data.  c.) The shape of the normal curve is controlled by the mode of the data.  d.) The shape of the normal curve is controlled by the mean of the data.  a.) Correct. Recall that the standard deviation is a shape/scale parameter for the normal distribution, so we can note that this is a true statement. At a nearby frozen yogurt shop, the mean cost of a pint of frozen yogurt is $1.50 with a standard deviation of $0.10. Assuming the data is normally distributed, approximately what percent of customers are willing to pay between $1.40 and $1.60 for a pint of frozen yogurt?  a.) 95%  b.) 99.7%  c.) 68%  d.) 34%  c.) Correct.

Since we know that the mean is 1.50 and the standard deviation is 0.10, we can note that both 1.40 and 1.60 are one standard deviation (1*0.10 = 0.10) away from 1.50. Assuming the data is normal, it should contain 68% of the data. The mean daily sales for February was $320 with a standard deviation of $50. On the 15th of February, the shop sold $340 of yogurt. Which month had a higher z-score for sales on the 15th, and what is the value of that z-score?  a.) February, with a z-score of 1.  b.) February, with a z-score of 0.4.  c.) January, with a z-score of 0.5.  d.) January, with a z-score of 0.2.  c.) Correct. Recall that . For January, . For February, . We can see that January had the higher z-score of 0.5. The standard deviation of any standard normal distribution is __________.  a.) 0  b.)

a.) Sample (n = 2) x̄ S 1  = {1, 1} 1 S 2  = {1, 2} 1.5 S 3  = {2, 2} 2 S 4  = {2, 3} 2.5 S 5  = {2, 4} 3 S 6  = {3, 4} 3.5  b.) Sample (n = 2) x̄ S 1  = {1, 1} 1 S 2  = {1, 2} 1.5 S 3  = {1, 3} 2 S 4  = {1, 4} 2.5 S 5  = {2, 3} 2.5 S 6  = {3, 4} 3.5  c.) Sample (n = 2) x̄ S 1  = {1, 2} 1.5 S 2  = {1, 3} 2 S 3  = {1, 4} 2.5 S 4  = {2, 3} 2.5 S 5  = {2, 4} 3 S 6  = {3, 4} 3.5  d.) Sample (n = 2) x̄ S 1  = {1, 1} 1

S 2  = {1, 2} 1.5 S 3  = {2, 2} 2 S 4  = {2, 3} 2.5 S 5  = {3, 3} 3 S 6  = {4, 4} 4  c.) Correct. Recall that the sampling distribution is the set of all possible samples of a given size for a given statistic. If we have 4 numbers and we draw 2, there are 6 possible samples we can draw. The samples are {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3.4}. We now take each sample and get the average. For example the sample (1,2) would have a mean of (1 + 2) / 2 = 3 / 2 = 1.5. Let x stand for the number of minutes spent at the mall. 100 people are sampled at a time. For the sampling distribution, the mean is 46 minutes and the standard deviation is 0.4 minutes. What is the mean and standard deviation of the population?  a.) mean = 46, standard deviation = 4  b.) mean = 4.6, standard deviation = 4  c.) mean = 46, standard deviation = 0.4  d.) mean = 4.6, standard deviation = 0.4  a.) Correct. The mean of the sampling distribution is equal to the population mean, which is 46. The standard deviation of the sampling distribution (0.4) is equal to the population standard deviation divided by the square root of the sample size (100):

 c.) 30  d.) 25  c.) Correct. In general, the Central Limit Theorem tells us for most distributions a sample size of 30 is enough to create a sampling distribution that is normal.