MATH 110 MODULE 4: Problem Set: Introduction to Statistics - Key - 2025B WITH FORMULA SHEET ON LAST PAGES Portage Learning

MATH 110 MODULE 4: Problem Set: Introduction to
Statistics - Key - 2025B WITH FORMULA SHEET ON LAST
PAGES Portage Learning
M4: Problem Set
• Due No due date
• Points 5
• Questions 8
• Time Limit None

Instructions

Attempt History
Attempt Time Score
LATEST Attempt 1 1,129 minutes 5 out of 5

Score for this quiz: 5 out of 5
Submitted Apr 20 at 10:41am This
attempt took 1,129 minutes.
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Question 1
pts

A barber expects to get between zero and six customers per hour in his barber shop. The probability of these
is given as follows:




Find the number of expected customers that the barber will get per hour. Also, find the variance and standard
deviation of this data.

, Your Answer:

We will calculate the expected number of customers, E(X), using the formula: E(X) = Σ [x * f(x)], where x is the
number of customers and f(x) is the probability.

Therefore, E(X) = (0 * 0.15) + (1 * 0.07) + (2 * 0.29) + (3 * 0.26) + (4 * 0.13) + (5 * 0.09) + (6 * 0.01) =
2.46

We will Calculate E(X²), using the formula: E(X²) = Σ [x² * f(x)

Therefore, ]E(X²) = (0² * 0.15) + (1² * 0.07) + (2² * 0.29) + (3² * 0.26) + (4² * 0.13) + (5² * 0.09) + (6² * 0.01) =
8.26

We will calculate the variance, Var(X), using the formula: Var(X) = E(X²) - [E(X)]².

Therefore, Var(X) = 8.26 - (2.46)² = 2.2084

We Calculate the standard deviation, SD, using the formula: SD = √Var(X) Therefore, SD

= √2.2084

= 1.486


Solution.

The expected value is given by




So, the barber can expect 2.46 customers per hour. The

variance is given by




The standard deviation is given by:




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Question 2
pts
A baseball player has a batting average of .211 (in other words, he gets a hit 21.1 % of the time that he goes up