Question

The average weight of a ball of pizza dough produced by the staff of a pizza parlor is 450.5 grams. As part of an attempt to monitor costs for raw ingredients, the owner of the pizza parlor randomly selects and weighs 34 balls of pizza dough. If the standard deviation for the weights of these balls of dough is 28.2 grams, what is the probability that a random sample of 34 balls of dough has a mean weight of more than 460 grams?  

Round your Z value(s) to two decimal places. Do not round any other intermediate calculations. Enter your answer as a decimal rounded to four places.

Probability =

Answer 1

given data

Population mean waight

number of sample taken (n)=34 (here sample size is >30 so we will perform Z test)

Standard daviation of the sample (S)=28.2

Sample mean waight

now we have to find the probablity of getting mean weight of the sample is more than 460 grams that is

Now for that lets calculate test statistic first

so from the formula of test statistic we have

so from the Standarrd probablity distribution table for Z score the probablity value for the degree of test statistic Z=1.96 is

since it is the area under the Z score so it is the probablity of getting mean weight lesss than 460 grams

S the probablity of getting mean sample weight more than 460 will be