In a spreadsheet, you can use the function NORM. DIST(upper bound, μ, σ, TRUE) to find the area under a normal curve for values of x less than or equal to a specified upper bound. Suppose the heights of all the children in a state are normally distributed with a mean of 41 inches and a standard deviation of 4 inches. What is the probability that a randomly chosen child is greater than 34 inches tall?

Given Information:

Mean height of children = μ = 41 inches

Standard deviation of height of children = σ = 4 inches

Required Information:

Using Excel find P(x > 34) = ?

P(x > 34) = 95.99%

Explanation:

What is Normal Distribution?

We are given a Normal Distribution, which is a continuous probability distribution and is symmetrical around the mean. The shape of this distribution is like a bell curve and most of the data is clustered around the mean. The area under this bell shaped curve represents the probability.  

The Microsoft Excel has a built-in function "NORMDIST" which calculates the probability of a normal distribution.

Syntax:

NORMDIST(x, mean, standard deviation, cumulative flag)  

Where x is the variable of interest

Cumulative flag = TRUE or FALSE

The probability that a randomly chosen child is greater than 34 inches tall is given by

P(x > 34) = 1 - P(x < 34)

Using MS Excel,

P(x > 34) = 1 - NORM.DIST(34,41,4,TRUE)

Which return the probability of

P(x > 34) = 1 - 0.040059

P(x > 34) = 0.959941

P(x > 34) = 95.99%

Therefore, there is 95.99% probability that a randomly chosen child is greater than 34 inches tall.

c 1 hour

step-by-step explanation:

m = 2e

m = 2 so 2 = 2e

1 = e

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.