A store manager is trying to decide whether to price oranges by weight, with a f

Question

A store manager is trying to decide whether to price oranges by weight, with a fixed cost per pound, or by the piece, with a fixed cost per orange. He is concerned that customers will choose the largest ones if there is a fixed price per orange. For one week the oranges are priced by the piece rather than by weight, and during this time the mean weight of the oranges purchased is recorded for all customers who buy 4 of them. The manager knows the population of weights of individual oranges is bell-shaped with mean of 8 ounces and a standard deviation of 1.6 ounces. Mean = 8ounces, S.D.= 0.8ounces What is the probability that the mean weight of 4 oranges exceeds 10 ounces?
A store manager is trying to decide whether to price oranges by weight, with a fixed cost per pound, or by the piece, with a fixed cost per orange. He is concerned that customers will choose the largest ones if there is a fixed price per orange. For one week the oranges are priced by the piece rather than by weight, and during this time the mean weight of the oranges purchased is recorded for all customers who buy 4 of them. The manager knows the population of weights of individual oranges is bell-shaped with mean of 8 ounces and a standard deviation of 1.6 ounces. Mean = 8ounces, S.D.= 0.8ounces What is the probability that the mean weight of 4 oranges exceeds 10 ounces?
A store manager is trying to decide whether to price oranges by weight, with a fixed cost per pound, or by the piece, with a fixed cost per orange. He is concerned that customers will choose the largest ones if there is a fixed price per orange. For one week the oranges are priced by the piece rather than by weight, and during this time the mean weight of the oranges purchased is recorded for all customers who buy 4 of them. The manager knows the population of weights of individual oranges is bell-shaped with mean of 8 ounces and a standard deviation of 1.6 ounces. Mean = 8ounces, S.D.= 0.8ounces What is the probability that the mean weight of 4 oranges exceeds 10 ounces?

Explanation / Answer

here std error of mean=std deviation/(n)1/2 =1.6/(4)1/2=0.8

hence probability that the mean weight of 4 oranges exceeds 10 ounces =P(X>10)

=1-P(X<10)=1-P(Z<(10-8)/0.8)=1-P(Z<2.5)=1-0.9938=0.0062

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