Let X be a normally distributed random variable with a mean of 20 and a standard deviation of 2.25. Using Excel, find the proportion of the values of X that are less than 21.

The normal distribution is the most important distribution. It describes well the

distribution of random variables that arise in practice, such as the heights or weights

of people, the total annual sales of a firm, exam scores etc. Also, it is important for the

central limit theorem, the approximation of other distributions such as the binomial,

etc.

• We say that a random variable X follows the normal distribution if the probability

density function of X is given by

f(x) = 1

σ

√

2π

e

− 1

2

(

x−µ

σ

)

2

, −∞ < x < ∞

This is a bell-shaped curve.

• We write X ∼ N(µ, σ). We read: X follows the normal distribution (or X is normally

distributed) with mean µ, and standard deviation σ.

Step-by-step explanation:

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;

∈3,600

step-by-step explanation: