**Question 1**

The heights of river birch trees are normally distributed with a mean of 92.3 inches and a standard deviation of 4.1 inches.

(d) What is the probability of a birch tree having a height that differs from the mean by at most 1 inch? Round answers to four decimal places.

Question 2

The monthly utility bills in a city are normally distributed, with a mean of

$100 and a standard deviation of $16.Find the probability that a randomly selected utility bill is(a) less than $66, (b) between $90 and $110, and (c) more than $120.

Question 3

The monthly utility bills in a city are normally distributed, with a mean of $100 and a standard deviation of $15.

Find the probability that a randomly selected utility bill is (a) less than $68, (b) between $84 and $110, and (c) more than $120.

Answer to question 1

Step 1

Given that the heights of a river birch trees are normally distributed with mean of 92.3 inches and a standard deviation of 4.1 inches.

Population mean, μμ =92.3

Population standard deviation,σσ =4.1

Compute the the probability of a birch tree having a height that differs from the mean by at most 1 inch.

Step 2

Thus, the probability of a birch tree having a height that differs from the mean by at most 1 inch is 0.1896.

The standard normal table is displayed below

Observe that the intersection part of 0.2 th row and 0.04th column, the area is 0.5948.

Observe that the intersection part of -0.2 th row and 0.04th column, the area is 0.4052.

Answer to question 2

Step 1

step 2

Answer to question 3

Step 1

Provided information is ;

Let X be the monthly utility bill

Step 2

Calculation :

Part b] :

Now we will find the Probability that monthly utility bill is between $84 and $110 as below ;

i.e we have to find P(84<X<110)

for that ;

firstly we have to find the z-score is given by ;