The amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and standard deviation 13 mL. Suppose that 43 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible. What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
If a single randomly selected individual is observed, find the probability that this person consumes is between 61.4 mL and 62.8 mL.
For the group of 43 pancake eaters, find the probability that the average amount of syrup is between 61.4 mL and 62.8 mL.
For part d), is the assumption that the distribution is normal necessary? No Yes
please only answer if you are able to answer all parts correctly

(a) X ~ N().

    ~ N().

(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is 0.0398.

(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is 0.2512.

(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.

Step-by-step explanation:

We are given that the amount of syrup that people put on their pancakes is normally distributed with mean 63 mL and a standard deviation of 13 mL.

Suppose that 43 randomly selected people are observed pouring syrup on their pancakes.

(a) Let X = amount of syrup that people put on their pancakes

The z-score probability distribution for the normal distribution is given by;

                      Z  =    ~ N(0,1)

where, = mean amount of syrup = 63 mL

            = standard deviation = 13 mL

So, the distribution of X ~ N().

Let = sample mean amount of syrup that people put on their pancakes

The z-score probability distribution for the sample mean is given by;

                      Z  =    ~ N(0,1)

where, = mean amount of syrup = 63 mL

            = standard deviation = 13 mL

            n = sample of people = 43

So, the distribution of ~ N().

(b) If a single randomly selected individual is observed, the probability that this person consumes is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < X < 62.8 mL)

   P(61.4 mL < X < 62.8 mL) = P(X < 62.8 mL) - P(X 61.4 mL)

  P(X < 62.8 mL) = P( < ) = P(Z < -0.02) = 1 - P(Z 0.02)

                                                           = 1 - 0.50798 = 0.49202

  P(X 61.4 mL) = P( ) = P(Z -0.12) = 1 - P(Z < 0.12)

                                                           = 1 - 0.54776 = 0.45224

Therefore, P(61.4 mL < X < 62.8 mL) = 0.49202 - 0.45224 = 0.0398.

(c) For the group of 43 pancake eaters, the probability that the average amount of syrup is between 61.4 mL and 62.8 mL is given by = P(61.4 mL < < 62.8 mL)

   P(61.4 mL < < 62.8 mL) = P( < 62.8 mL) - P( 61.4 mL)

  P( < 62.8 mL) = P( < ) = P(Z < -0.10) = 1 - P(Z 0.10)

                                                           = 1 - 0.53983 = 0.46017

  P( 61.4 mL) = P( ) = P(Z -0.81) = 1 - P(Z < 0.81)

                                                           = 1 - 0.79103 = 0.20897

Therefore, P(61.4 mL < X < 62.8 mL) = 0.46017 - 0.20897 = 0.2512.

(d) Yes, for part (d), the assumption that the distribution is normally distributed necessary.

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.  

c 1 hour

step-by-step explanation:

m = 2e

m = 2 so 2 = 2e

1 = e