an orange juice producer buys oranges from a large orange grove that has one variety of orange. the amount of juice squeezed from these oranges is approximately normally distributed, with a mean of 4.70 ounces and a standard deviation of 0.40 ounce. suppose that you select a sample of 25 oranges. the probability is 0.77 that the sample mean amount of juice will be greater than what value?

Question

contestada

Respuesta :

lhhypoliteitodo lhhypoliteitodo · Answer 1 · 2022-11-26T13:08:47+01:00

When the probability is 0.77 for the sample mean to be greater than certain value, tis value is solved to be 4.3

The problem will be solved with t-scores as the number of sample is less than 30

number of sample, n = 25

degree of freedom, df

= n - 1

= 25 - 1 = 24

Assuming a confidence level of 95%, probability of 0.77, with a df of 24 the t-score is 2.064

the question is asking for greater than = 1 - 2.064 = -1.064

Using the formula for t scores

t = (X - μ) / σ

Definition of variables

mean, μ = 4.70

standard deviation, σ = 0.40

-1.064 = (X - 4.7)/0.4

-1.064 * 0.4 = X - 4.7

-0.4256 = X - 4.7

-0.4256 + 4.7 = X

X = 4.2744 approximately 4.3

Learn more about t-scores at:

https://brainly.com/question/6501190

#SPJ1