A survey of 50 retail stores revealed that the average price of a microwave was $375, with a sample standard deviation of $20 (i. e. the population standard deviation was not known). Assuming the population is normally distributed, what is the 95% confidence interval to estimate the true cost of the microwave? a) $323.40 to $426.60b) $328.40 to $421.60c) $350.80 to $395.80d) $369.31 to $380.69

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Mathematics

Kyra Faulkner

Yesterday, 21:38

A survey of 50 retail stores revealed that the average price of a microwave was $375, with a sample standard deviation of $20 (i. e. the population standard deviation was not known). Assuming the population is normally distributed, what is the 95% confidence interval to estimate the true cost of the microwave? a) $323.40 to $426.60b) $328.40 to $421.60c) $350.80 to $395.80d) $369.31 to $380.69

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Junior Pruitt · Answer 1

Answer: d) $369.31 to $380.69

Step-by-step explanation:

Given;

Mean price x = $375

Standard deviation r = $20

Number of retail stores n = 50

Confidence interval of 95%

Z * (95%) = 1.96

Confidence interval = x+/-Z * (r/√n)

= $375+ / - 1.96 (20/√50)

= $375+ / - 5.69

Confidence interval = ($369.31 to $380.79)