type the correct answer in each box. use numerals instead of words.\na company manufactures 2,000 units of…

type the correct answer in each box. use numerals instead of words.\na company manufactures 2,000 units of its flagship product in a day. the quality control department takes a random sample of 40 units to test for quality. the product is put through a wear - and - tear test to determine the number of days it can last. if the product has a lifespan of less than 26 days, it is considered defective. the table gives the sample data that a quality control manager collected.\n39 31 38 40 29\n32 33 39 35 32\n32 27 30 31 27\n30 29 34 36 25\n30 32 38 35 40\n29 32 31 26 26\n32 26 30 40 32\n39 37 25 29 34\nthe point estimate of the population mean is , and the point estimate of the proportion of defective units is

type the correct answer in each box. use numerals instead of words.\na company manufactures 2,000 units of its flagship product in a day. the quality control department takes a random sample of 40 units to test for quality. the product is put through a wear - and - tear test to determine the number of days it can last. if the product has a lifespan of less than 26 days, it is considered defective. the table gives the sample data that a quality control manager collected.\n39 31 38 40 29\n32 33 39 35 32\n32 27 30 31 27\n30 29 34 36 25\n30 32 38 35 40\n29 32 31 26 26\n32 26 30 40 32\n39 37 25 29 34\nthe point estimate of the population mean is , and the point estimate of the proportion of defective units is

Answer

Explanation:

Step1: Calculate the sum of all data points.

The data points are: 39, 31, 38, 40, 29 32, 33, 39, 35, 32 32, 27, 30, 31, 27 30, 29, 34, 36, 25 30, 32, 38, 35, 40 29, 32, 31, 26, 26 32, 26, 30, 40, 32 39, 37, 25, 29, 34 Sum = $39+31+38+40+29+32+33+39+35+32+32+27+30+31+27+30+29+34+36+25+30+32+38+35+40+29+32+31+26+26+32+26+30+40+32+39+37+25+29+34 = 1292$

Step2: Calculate the point estimate of the population mean.

The sample size $n = 40$. The point estimate of the population mean is the sample mean $\bar{x}$. $$ \bar{x} = \frac{\text{Sum of data values}}{n} $$ $$ \bar{x} = \frac{1292}{40} = 32.3 $$

Step3: Identify the number of defective units.

A unit is defective if its lifespan is less than 26 days. From the data, the values less than 26 are 25 (occurs twice). Number of defective units = 2.

Step4: Calculate the point estimate of the proportion of defective units.

The point estimate of the proportion of defective units is the sample proportion $\hat{p}$. $$ \hat{p} = \frac{\text{Number of defective units}}{\text{Sample size}} $$ $$ \hat{p} = \frac{2}{40} = \frac{1}{20} = 0.05 $$

Answer:

The point estimate of the population mean is 32.3, and the point estimate of the proportion of defective units is 0.05.