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Brut [27]
3 years ago
11

The amount of icing on a Cuppie Cake large cupcake follows a Normal distribution, with a mean of 2 ounces and a standard deviati

on of 0.3 ounce. A random sample of 16 cupcakes is selected every day and measured. What is the probability the mean weight will exceed 2.1 ounces?
Mathematics
1 answer:
TiliK225 [7]3 years ago
6 0

Answer: the probability the mean weight will exceed 2.1 ounces is 0.09

Step-by-step explanation:

Let x be the random variable representing the amount of icing on a Cuppie Cake large cupcake. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = standard deviation

n = number of samples

From the information given,

µ = 2

σ = 0.3

n = 16

x = 2.1

the probability that the mean weight will exceed 2.1 ounces is expressed as

P(x ≥ 2.1)

For x = 2.1

z = (2.1 - 2)/(0.3/√16) = 1.33

We would determine the probability for the area above z = 1.33 from the normal distribution table. It would be

p = 1 - 0.91 = 0.09

P(x ≥ 2.1) = 0.09

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Explicit formulas for arithmetic sequences are derived from terms in arithmetic sequences. It helps to find each term in arithmetic progression easily. The arithmetic progression is a1, a2, a3, ..., an. where the first term is denoted as 'a', we have a = a1, and the tolerance is denoted as 'd'. The tolerance formula is d = a2 - a1 = a3 - a2 = an - an - 1. The nth term of the arithmetic progression represents the explicit formula for the arithmetic progression.

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