Question

The average weight of a ball of pizza dough produced by the staff of a pizza parlor is 459.5 grams. As part of an attempt to monitor costs for raw ingredients, the owner of the pizza parlor randomly selects and weighs 52 balls of pizza dough. If the standard deviation for the weights of these balls of dough is 30.0 grams, what is the probability that a random sample of 52 balls of dough has a mean weight of more than 462 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

Solution :

Given that ,

mean = = 459.5

standard deviation = = 30.0

n = 50

= 459.5

= / n = 30.0/ 50= 4.2426

P( > 462 ) = 1 - P( < 462 )

= 1 - P[( - ) / < ( 462-459.5) / 4.2426 ]

= 1 - P(z <0.59 )

Using z table

= 1 - 0.7224

= 0.2776

probability=0.2776