The heights in centimetres of men in a sample selected at random may be modelled by a normal distribution with mean 180.5 and standard deviation 11.3.

1 Choose the option that is closest to the value above which 30% of the heights of men will lie.
Options for Question1
A 174.57 B 180.32 C 180.50 D 186.43 E 198.33 F 200.50
2 Choose the option that is closest to a range of values,symmetric
about the mean, within which the heights of approximately 80% of
men will lie.
Options for Question 2
A (157.0, 194.0) B (159.2, 201.8) C (167.8, 193.2) D (163.0, 198.0) E (166.0, 195.0) F (168.7, 192.2)
3 Choose the option that is closest to the percentage of heights of men below 170 cm.
Options for Question 3
A 17% B 18% C 19% D 40% E 41% F 42%

Use the second applet for your question

http://davidmlane.com/hyperstat/z_table.html

It is more accurate than tables and you don't even have to convert to z-scores.

does it mean that:

1. is D
2. is E
3. is B ?
Regards.

To answer these questions, we need to use the properties of the normal distribution. The normal distribution is a continuous probability distribution that is symmetric and bell-shaped.

1. To find the value above which 30% of the heights of men will lie, we need to find the corresponding z-score. The z-score represents the number of standard deviations away from the mean a particular value is.

We can use the standard normal distribution table (also known as the Z-table) to find the corresponding z-score. The Z-table provides the cumulative probability to the left of a given z-score. However, since we want the percentage above the value, we'll use the cumulative probability to the right of the z-score.

The formula to find the z-score is:
z = (x - μ) / σ

where:
x = the value we want to find the z-score for (in this case, the value above which 30% of heights will lie)
μ = the mean of the distribution
σ = the standard deviation of the distribution

Calculating the z-score:
z = (x - 180.5) / 11.3

Now, let's find the z-score from the Z-table. Look for the cumulative probability closest to 0.30 in the right column of the table. The corresponding z-score is the one in the left column.

The correct answer would be the option that matches the calculated z-score.

2. To find the range of values within which approximately 80% of the heights of men will lie, we need to use the concept of z-scores and the Standard Deviation Rule.

According to the Standard Deviation Rule, approximately 68% of the data falls within 1 standard deviation from the mean, approximately 95% falls within 2 standard deviations from the mean, and approximately 99.7% falls within 3 standard deviations from the mean.

Since we want to find the range within which 80% of the data falls, we need to go 1 standard deviation to the left and 1 standard deviation to the right from the mean.

The range of values can be calculated using the formula:
Range = (μ - σ, μ + σ)

where μ = mean and σ = standard deviation.

The correct answer would be the option that matches the calculated range.

3. To find the percentage of heights of men below 170 cm, we need to find the cumulative probability at that specific value using the Z-table.

The formula to find the cumulative probability is:
P(X ≤ x) = Φ((x - μ) / σ)

where:
x = the value we want to find the cumulative probability for (in this case, 170 cm)
μ = the mean of the distribution
σ = the standard deviation of the distribution
Φ = cumulative distribution function

Find the value closest to 170 cm in the Z-table and match it with the corresponding cumulative probability given. The correct answer would be the option that matches the calculated percentage.

Note: The Z-table may not exactly match the given options, so you may need to choose the closest value.