Quiz about Data Science pnorm, qnorm (Lab 2I)

Question 1

What does the `pnorm` function calculate in statistics?

Accepted Answer

The probability of observing a value less than or equal to a given value in a normal distribution.

Answer

The percentile of a given value in a normal distribution.

Answer

The mean of a normal distribution.

Answer

The standard deviation of a normal distribution.

Question 2

If the mean ( $$\mu$$ ) of a normal distribution is 100, the standard deviation ( $$\sigma$$ ) is 15, and the value ( $$x$$ ) is 115, what is the `pnorm` of $$x$$ ?

Accepted Answer

0.8413

Answer

0.9082

Answer

0.9332

Answer

0.9772

Question 3

What does the `qnorm` function calculate in statistics?

Accepted Answer

The value at a given percentile in a normal distribution.

Answer

The probability of observing a value less than or equal to a given value in a normal distribution.

Answer

The mean of a normal distribution.

Answer

The standard deviation of a normal distribution.

Question 4

If you want to find the 95th percentile of a normal distribution with a mean ( $$\mu$$ ) of 50 and a standard deviation ( $$\sigma$$ ) of 10, what is the `qnorm` of this percentile?

Accepted Answer

66.45

Answer

60.815

Answer

70.1

Answer

73.5

Question 5

What does calculating `1 - pnorm` for a given value in a normal distribution represent?

Accepted Answer

The probability of observing a value greater than the given value.

Answer

The mean of the normal distribution.

Answer

The standard deviation of the normal distribution.

Answer

The percentile of the given value in the normal distribution.

Question 6

If the mean ( $$\mu$$ ) of a normal distribution is 0, the standard deviation ( $$\sigma$$ ) is 1, and the value ( $$x$$ ) is 2, what is `1 - pnorm` of $$x$$ ?

Accepted Answer

0.0228

Answer

0.1587

Answer

0.9772

Answer

0.8413

Question 7

In the context of quality control, how can `pnorm` be used in a real-world application?

Accepted Answer

To determine the probability of a product's dimension being within the specified tolerance levels.

Answer

To calculate the mean time until a machine fails.

Answer

To find the maximum capacity of a production line.

Answer

To calculate the total revenue from sales.

Question 8

If a test score is normally distributed with a mean ( $$\mu$$ ) of 75 and a standard deviation ( $$\sigma$$ ) of 10, what is the probability that a randomly selected test score is less than 90?

Accepted Answer

0.9332

Answer

0.8413

Answer

0.9772

Answer

0.9082

Question 9

For a normal distribution with a mean ( $$\mu$$ ) of 100 and a standard deviation ( $$\sigma$$ ) of 20, what value corresponds to the 25th percentile?

Accepted Answer

86.51

Answer

84.13

Answer

92.07

Answer

95.45

Question 10

A fuel pump at a gasoline station doesn't always dispense the exact amount displayed on the meter. When the meter reads 1.00 L , the amount of fuel a certain pump dispenses is normally distributed with a mean of 1 L standard deviation of 0.05 L . Find the probability that amount dispensed in a random trial is less than or equal to 1.05 L.

Accepted Answer

84%

Answer

0.16 %

Answer

16%

Answer

0.84%

Question 11

A set of biology exam scores are normally distributed with a mean of 70 points and a standard deviation of 6 points. Joey wants to know, what is the probability that he earned a 90 A or HIGHER. (hint: use 1 - pnorm since it says "or HIGHER")

Accepted Answer

0.0004290603

Answer

0.9995709

Answer

0.02275013

Answer

0.01513014

Question 12

Given a normal distribution with a mean ( $$\mu$$ ) of 30 and a standard deviation ( $$\sigma$$ ) of 5, what is the `qnorm` for the 80th percentile?

Accepted Answer

34.20

Answer

34.15

Answer

36.2

Answer

37.5

Question 13

For a dataset following a normal distribution with a mean ( $$\mu$$ ) of 120 and a standard deviation ( $$\sigma$$ ) of 15, calculate the `pnorm` for a value ( $$x$$ ) of 135.

Accepted Answer

0.8413

Answer

0.9082

Answer

0.9332

Answer

0.9772

Question 14

What is the probability that a measurement is more than 1.5 standard deviations above the mean in a normal distribution?

Accepted Answer

0.0668

Answer

0.9332

Answer

0.1292

Answer

0.8708

Question 15

A set of middle school student heights are normally distributed with a mean of 150 centimeters and a standard deviation of 20 centimeters. Find the probability of randomly selecting a student that is 115 cm or less?

Accepted Answer

0.04

Accepted Answer

4%

Answer

0.05

Answer

5%

Data Science pnorm, qnorm (Lab 2I)

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