Question

A. The average charitable contribution itemized per income tax return in a certain state is $792. Suppose that the distribution of contributions is normal with a standard deviation of $103. Find the limits for the middle 80% of contributions. Round z-value calculations and final answers to 2 decimal places.B. For a certain group of individuals, the average heart rate is 70 beats per minute. Assume the variable is normally distributed and the standard deviation is 3 beats per minute. If a subject is selected at random, find the probability that the person has the following heart rate. Round the final answers to at least four decimal places and intermediate z-value calculations to two decimal places. Higher than 68 beats per minute

Answer 1

Let x be a random variable representing heart rates of individuals in a certain group. Given that the heart rates are normally distributed, we would calculate the z score by applying the formula for calculating z score which is expressed as

z = (x - μ)/σ

where

x is the sample mean

μ is the population mean

σ is the population standard deviation

From the information given,

μ = 70

σ = 3

x = 68

By substituting these values into the formula,

z = (68 - 70)/3 = 0.67

We want to find the probability that a randomly selected individual has a heart rate greater than 68 beats per minute. This is represented as

P(x > 68)

This can also be written as 1 - P(x ≤ 68)

We would find the probability value corresponding to a z score of 0.67 from the standard normal distribution table. It is

P(x ≤ 68) = 0.74857

Thus,

P(x > 68) = 1 - 0.74857 = 0.25143

Rounding to