Question 1

0 / 6 points

A carpenter wants to know the average length of the wooden planks they have in their workshop. They measure 12 planks and get the following lengths in inches: 24, 36, 18, 30, 24, 30, 36, 18, 24, 36, 30, 18 Calculate the mean and sample standard deviation (3 decimal places) for this set of values.

Enter the mean length

___30___

Now enter the sample standard deviation (up to 3 decimal places)

___8.092___

Question 2

6 / 6 points

A clothing store sells t-shirts in two sizes: small and medium. The store manager claims that 70% of their customers buy a medium-sized t-shirt. Assuming a binomial distribution, what is the probability that out of 100 customers, 60 or more will buy a medium-sized t-shirt? (show answer up to 2 decimal places)

Answer:

0.99

Question 3

0 / 6 points

A coffee shop owner wants to estimate the average time their customers spend in the shop. They sample 40 customers and find that the sample mean time is 45 minutes with a sample standard deviation of 10 minutes. What is the 95% confidence interval for the mean time that all customers spend in the shop?

What is the lower value? (up to 2 decimal places)

___41.90___

What is the upper value? (up to 2 decimal places)

___48.10___

Question 4

1.5 / 6 points

A company claims that their new software can process data on average in less than 5 seconds with a standard deviation of 1.5 seconds. A software engineer tests the software on 25 different occasions and finds that the sample mean time to process data is 4.2 seconds. Is there evidence to support the company's claim (yes or no)? (Use a one-tailed test with a significance level of 0.05.)

What is the t-value?

___-2.666667___

What is the p-value?

___0.00675___

What is the critical t-value?

___-1.710882___

Is there evidence to support the company's claim (yes or no)?

___yes___

Question 5

6 / 6 points

A bakery wants to know how many cupcakes they should prepare each day to meet the demand. They have collected data for the past 30 days and found that the daily demand for cupcakes follows a normal distribution with a mean of 120 and a standard deviation of 15. What is the minimum number of cupcakes the bakery should prepare each day to meet the demand 90% of the time?

Answer:

140