The coffee and soup machine at the local subway station is supposed to fill cups with 6 ounces of soup. ten cups of soup are bought with results of a mean of 5.93 ounces and a standard deviation of 0.13 ounces. how large a sample of soups would we need to be 95 percent confident that the sample mean is within 0.03 ounces of the population mean?

sample size is 73

Step-by-step explanation:

Given data

mean = 5.93

standard deviation = 0.13

confident = 95%

sample mean = 0.03

top find out

sample of soups

solution

we know Z critical value is  1.96 with the help of Z table when a = 0.05 ( 95 % confident)  and sample mean is 0.03

so sample = (( Z × standard deviation  ) / sample mean)^2    1

so now put all value  Z ,  standard deviation and sample mean in equation 1

sample = (( Z × standard deviation  ) / sample mean)^2

sample = (( 1.96 ×  0.13  ) / 0.03)^2

sample = 72.137

so sample size is 73

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.