The average American man consumes 9.6 grams of sodium each day. Suppose that the sodium consumption of American men is normally distributed with a standard deviation of 1 grams. Suppose an American man is randomly chosen. Let X = the amount of sodium consumed. Round all numeric answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N(
,
)

b. Find the probability that this American man consumes between 9.1 and 10.7 grams of sodium per day.

c. The middle 30% of American men consume between what two weights of sodium?
Low:

High:

In 93.12% of the samples the sample mean height would be between 135 and 155 cm

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation , the sample means with size n can be approximated to a normal distribution with mean and standard deviation

In this problem, we have that:

In what percentage of the samples would the sample mean height be between 135 and 155 cm?

This is the pvalue of Z when X = 155 subtracted by the pvalue of Z when X = 135. So

X = 155

By the Central Limit Theorem

has a pvalue of 0.9656

X = 135

has a pvalue of 0.0344

0.9656 - 0.0344 = 0.9312

In 93.12% of the samples the sample mean height would be between 135 and 155 cm