Question

Q1

1. Under the standard normal curve, find the area to the right of z = 2.15
2. Under the standard normal curve, find the area to the right of z = -2.50
3. Under the standard normal curve, find the area to the left of z = -1.63
4. Under the standard normal curve, find the area to the left of z = 1.30
5. Under the standard normal curve, find the area more extreme than z = ±0.85, that is, more than 0.85 standard deviations away from the mean (< z = -0.85 or > z = 0.85)
6. Under the standard normal curve, find the area between z = -1.63 and z = 2.15
7. Under the standard normal curve, find the area between z = -2.50 and z = -1.63
8. Under the standard normal curve, find the area between z = 1.30 and z = 2.15
1. What z-score on the standard normal curve has an area of 0.1151 to its right?
10. What z-score on the standard normal curve has an area of 0.6443 to its right?
11. What z-score on the standard normal curve has an area of 0.3372 to its left?
50. What z-score on the standard normal curve has an area of 0.8980 to its left?
1000. If a distribution is normally distributed with mean 100 and standard deviation 15, what score has 20 percent of the distribution below it?
14. If a distribution is normally distributed with mean 100 and standard deviation 15, what proportion of the scores fall at 118 or above?

Answer 1

(a) Under the standard normal curve, find the area to the right of .

The area to the right of is,

{Since }

From the z table, the probability value is the value with corresponding row 2.1 and column 0.05.

  

Thus the area to the right of z = 2.15 is .

(b) Under the standard normal curve, find the area to the right of .

The area to the right of is,

{Since }

From the z table, the probability value is the value with corresponding row 2.5 and column 0.00.

  

Thus the area to the right of is .

(c) Under the standard normal curve, find the area to the left of .

The area to the left of is,

From the z table, the probability value is the value with corresponding row -1.6 and column 0.03.

Thus the area to the left of is .

(d) Under the standard normal curve, find the area to the left of .

The area to the left of is,

From the z table, the probability value is the value with corresponding row 1.3 and column 0.00.

Thus the area to the left of is .

(e) Under the standard normal curve, find the area more extreme than z = ±0.85, that is, more than 0.85 standard deviations away from the mean (< z = -0.85 or > z = 0.85)

The area more extreme than z = ±0.85 is,

{Since }

From the z table, the first probability value is the value with corresponding row 0.8 and column 0.05 and the second probability value is the value with corresponding row -0.8 and column 0.05.

Thus the area more extreme than z = ±0.85 is .

(f) Under the standard normal curve, find the area between and .

The area between and is,

  

{Since }

From the z table, the first probability value is the value with corresponding row 2.1 and column 0.05 and the second probability value is the value with corresponding row -1.6 and column 0.03.

Thus the area between and is .

(g) Under the standard normal curve, find the area between and .

The area between and is,

  

{Since }

From the z table, the first probability value is the value with corresponding row -1.6 and column 0.03 and the second probability value is the value with corresponding row -2.5 and column 0.00.

  

Thus the area between and is .

(h) Under the standard normal curve, find the area between and .

The area between   and is,

  

{Since }

From the z table, the first probability value is the value with corresponding row 2.1 and column 0.05 and the second probability value is the value with corresponding row 1.3 and column 0.00.

Thus the area between and is .

(i) What z-score on the standard normal curve has an area of 0.1151 to its right?

The z-score on the standard normal curve that has an area of 0.1151 to its right is,

From the z table, the probability value 0.8849 has the corresponding row 1.2 and column 0.00. Thus the z score is .

The z-score on the standard normal curve that has an area of 0.1151 to its right is .

(j) What z-score on the standard normal curve has an area of 0.6443 to its right?

The z-score on the standard normal curve that has an area of 0.6443 to its right is,

From the z table, the probability value 0.3557 has the corresponding row -0.3 and column 0.07. Thus the z score is .

The z-score on the standard normal curve that has an area of 0.6443 to its right is .

(k) What z-score on the standard normal curve has an area of 0.3372 to its left?

The z-score on the standard normal curve that has an area of 0.3372 to its left is,

From the z table, the probability value 0.3372 has the corresponding row -0.4 and column 0.02. Thus the z score is .

The z-score on the standard normal curve that has an area of 0.3372 to its left is .

(ax) What z-score on the standard normal curve has an area of 0.8980 to its left?

The z-score on the standard normal curve that has an area of 0.8980 to its left is,

From the z table, the probability value 0.8980 has the corresponding row 1.2 and column 0.07. Thus the z score is .

The z-score on the standard normal curve that has an area of 0.8980 to its left is .

(all) If a distribution is normally distributed with mean 100 and standard deviation 15, what score has 20 percent of the distribution below it?

Since 20 percent of the score's distribution below it, the probability value is .

Given the mean and standard deviation .

From the z table, the probability value 0.20 has the corresponding row -0.8 and column 0.04. Thus the z score is .

To find the score we will use the z score formula given by,

If a distribution is normally distributed with mean 100 and standard deviation 15, the score that has 20 percent of the distribution below it is .

(n) If a distribution is normally distributed with mean 100 and standard deviation 15, what proportion of the scores fall at 118 or above?

Given the mean and standard deviation .

To find the proportion we use the z score formula given by,

The proportion of the scores fall at 118 or above is,

(Since }

From the z table, the probability value is the value with corresponding row 1.2 and column 0.00

  

The proportion of the scores fall at 118 or above is .