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11. Following are the number of grams of carbohydrates in a 12 oz espresso beverage offered at Starbucks.
14 43 38 44 31 27 39 59 9 10 54
14 25 26 9 46 30 24 41 26 27 14
a) Find the first and third quartiles of these data. _____________, ______________
b) Find the median ___________________
c) Find the upper and lower boundaries: Upper _______________, Lower ______________
d) The beverage with the most carbohydrates is a Peppermint White Chocolate Mocha with 59 grams is this an outlier? _________________________
e) Construct a boxplot of the data.
f) Describe the shape of the distribution.
P(X= -2)= P(X= -1), P(X= 2)= P(X= 1) and
P(X> 0)=P(X< 0)= P(X= 0).
Obtain the probability mass function of X and its distribution function.
2.A.random variable X assumes the values -3, -2, -1,0, 1,~, 3 such that
P(X= -3)= P(x= -2)= P(X= -1),
P(X= 1)= P(X= 2)= P(X= 3),
and P ( X= 0) = P ( X > 0) = P ( X < 0),
Obtain the probability mass function of X and 'its distribution function, and find
further the probability mass function of Y = 2X^2 + 3X + 4.
(a) A random variable X has the following probability function
.x : -2 -1 0 1 2 3
p(x): 0.1 k 0·2 2k 0·3 k
(i) Find the value of k. and calculate mean and variance.
(ii) construct the cumulative distribution function c.d.f F(x) and draw its graph.
find the probability that 1. both are black
a. Find the sample proportion of customers who believe ATM machines should offer postage stamps.
b. Find a 99% confidence interval for the true proportion of customers who believe ATM machines should offer postage stamps.
c. A bank official claims the proportion of customers who believe ATM machines should offer postage stamps is 0.60. Is there any evidence to refute this claim? Test at the 5% level
d. If you test at the 1% level, what would be your decision?
Χ = Salad plate filling weight.
i. Find the probability density function of Χ
ii. What is the probability that a customer will take between 12 and 15 ounces of salad? iii. What is the probability that a customer will take fewer than 5 ounces of salad.
iv. Find Ε ( Χ) and Var ( Χ)
#340153 on Dec 2023