# Question: The diameters of Red Delicious apples in a certain orchard

The diameters of Red Delicious apples in a certain orchard are normally distributed with a mean of 2.63 inches and a standard deviation of 0.25 inch.

a. What percentage of the apples in this orchard have diameters less than 2.25 inches?

b. What percentage of the apples in this orchard are larger than 2.56 inches in diameter? A random sample of 100 apples is gathered, and the mean diameter obtained is x = 2.56

c. If another sample of size 100 is taken, what is the probability that its sample mean will be greater than 2.56 inches?

e. Why is the formula for the z-score used in part c different from that used in parts a and b?

a. What percentage of the apples in this orchard have diameters less than 2.25 inches?

b. What percentage of the apples in this orchard are larger than 2.56 inches in diameter? A random sample of 100 apples is gathered, and the mean diameter obtained is x = 2.56

c. If another sample of size 100 is taken, what is the probability that its sample mean will be greater than 2.56 inches?

e. Why is the formula for the z-score used in part c different from that used in parts a and b?

**View Solution:**## Answer to relevant Questions

a. Find a value for e such that 95% of the apples in Exercise 7. 50 are within e units of the mean, 2.63. That is, find e such that b. Find a value for E such that 95% of the samples of 100 apples taken from the orchard in ...A report in The Washington Post (April 26, 2009) stated that the average age for men to marry in the United States is now 28 years of age. If the standard deviation is assumed to be 3.2 years, find the probability that a ...A pop music record firm wants the distribution of lengths of cuts on its records to have an average of 2 minutes and 15 seconds (135 seconds) and a standard deviation of 10 seconds so that disc jockeys will have plenty of ...A random sample of 50 female American health professionals yielded the following height data. a. What population was sampled to obtain the height data listed above? b. Describe the sample data using the mean and standard ...Find the value of z for each of the following: a. Ho: µ = 35 versus Ha: µ > 35 when p-value = 0.0582 b. Ho: µ = 35 versus Ha: µ < 35 when p-value = 0.0166 c. Ho: m_35 versus Ha: µ = 35 when p-value = 0.0042Post your question