The average resting heart rate of a population is 90 beats per minute, with a standard deviation of 10.5 bpm. Find the z-scores that correspond to each of the following heart rates. Round your answers to the nearest hundredth, if necessary.

(a) 113 bpmz = (b) 78 bpmz = Detailed Answer: Understanding Z-Scores: Analyzing Resting Heart Rates Z-scores are an essential concept in statistics, helping us understand how individual values compare to the overall population mean. They measure how many standard…

A soft drink manufacturer wishes to know how many soft drinks teenagers drink each week. They want to construct a 90% confidence interval with an error of no more than 0.07. A consultant has informed them that a previous study found the mean to be 7.4 soft drinks per week and found the variance to be 0.81. What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.

Answer: Given Data: A confidence interval $( CI) = 0.90 $ A margin of error $( E) = 0.07 $ A population mean $ (\mu) = 7.4 $ A population variance $ (\sigma^2) = 0.81 $ A minimum sample size…

The average amount of money spent for lunch per person in the college cafeteria is $5.5$ and the standard deviation is $2.97.$ Suppose that 16 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.

(a) What is the distribution of X? X ~ N(,) (b) What is the distribution of x̄? x̄ ~ N(,) (c) For a single randomly selected lunch patron, find the probability that this patron’s lunch cost is between $5.9663 and…

The mean output of a certain type of amplifier is 495 watts with a variance of 100. If 85 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by more than 0.9 watts? Round your answer to four decimal places.

Answer:Given Data : The population mean $ (μ)=495 $ The population standard deviation $ (σ)= \sqrt(100) =10 $ The sample size $(n) = 85 $ olution: The probability that the mean of the sample would differ from the population mean…