You are considering a beam design that has dimensions of b = 14 in., h = 30 in., and d = 27.5 in. The beam is singly reinforced with all of the reinforcement in a single row. The concrete strength is 10,000 psi, and the yield strength of the reinforcement is 60,000 psi. What cross-sectional area of reinforcement is needed to achieve a strain in the reinforcement of 0.0075?

You are considering a beam design that has dimensions of b = 14 in., h = 24 in., and d = 21.5 in. The beam is singly reinforced with all of the reinforcement in a single row. The concrete strength is 6,700 psi, and the yield strength of the reinforcement is 60,000 psi. What cross-sectional area of reinforcement is needed to achieve a strain in the reinforcement of 0.0075?

A beam has dimensions of b = 18 in., h = 22 in., and d = 19.5 in. and is reinforced with 5 No. 7 bars. The concrete strength is 7,600 psi, and the yield strength of the reinforcement is 60,000 psi. Assuming the reinforcement has yielded, determine the tensile force T in the reinforcement.

A beam has dimensions of b = 18 in., h = 28 in., and d = 25.5 in. and is reinforced with 4 No. 7 bars. The concrete strength is 3,100 psi, and the yield strength of the reinforcement is 60,000 psi. Assuming the reinforcement has yielded, determine the depth to the neutral axis, c.

(05.04 HC)  A program was created to randomly choose customers at a sporting goods store to receive a discount. The program claims 25% of the receipts will get a discount in the long run. The manager of the sporting goods store is skeptical and believes the program’s calculations are incorrect. She selects a random sample and finds that 22% received the discount. The confidence interval is 0.22 ± 0.04 with all conditions for inference met. Part A: Using the given confidence interval, is it statistically evident that the program is not working? Explain. (3 points)Part B: Is it statistically evident from the confidence interval that the program creates the discount with a 0.25 probability? Explain. (2 points)Part C: Another random sample of receipts is taken. This sample is four times the size of the original. Twenty-two percent of the receipts in the second sample received the discount. What is the value of margin of error based on the second sample with the same confidence level as the original interval? (2 points)Part D: Using the margin of error from the second sample in part C, is the program working as planned? Explain. (3 points) (10 points)

(05.01 MC)  Suppose we select a simple random sample of size n = 325 from a large population with a proportion p of successes. Let p̂ be the proportion of successes in the sample. For which value of p is it appropriate to use the Normal approximation for the sampling distribution of p̂? (4 points)

If ones goal of a resistance training program is to hypertrophy train (improve both endurance and strength) about what % of intensity should they be spending the majority of time lifting at.  

(05.02 MC)  The amount of marinara sauce on the spaghetti at Pasta Infusion follows a Normal distribution, with a mean of 3.25 ounces and a standard deviation of 0.2 ounce. A random sample of 10 plates of spaghetti is selected every day and the sauce is measured. What is the probability that the mean weight will exceed 3.3 ounces? (4 points)

(05.02 MC)  A nail fabrication machine makes nails with a target length of μ = 2.35 inches. The machine has some variability, so the standard deviation of the length is σ = 0.2 inch. The machine operator inspects a random sample of 10 nails each hour for quality control purposes and records the sample mean diameter, x̄. Assuming the process is working properly, what are the mean and standard deviation of the sampling distribution of x̄? (4 points)

(05.01 LC)  Tiara, a quality assurance inspector at a chocolate factory, checks for product quality using a random sample of 18 pieces of chocolate from a batch of 60, with 17 white chocolates and 43 dark chocolates. Let p̂ be the proportion of white chocolates in the sample. Part A: Is the 10% condition met in this case? Justify your answer. (5 points) Part B: Is the Normal condition met in this case? Justify your answer. (5 points) (10 points)