The life span of a graphing calculator manufactured by Texas Instruments has a normal distribution with a mean of 54 months and a standard deviation of 8 months. The company guarantees that any calculator that starts malfunctioning within 36 months of the purchase will be replaced by a new one. You apply the normal model and discover that this is approximately 1.22% of their graphing calculators. Texas Instruments has sold 75 million graphing calculators world- wide. How many of these would you expect to malfunction within 3 months (and thus need to be replaced)? Explain.

The expected number of graphing calculators that malfunctions within 3 months and need to be replaced is 915,000.

Step-by-step explanation:

Let X represents the number of graphing calculator that starts malfunctioning within 36 months of the purchase and needs to be replaced by a new one.

It is provided that X follows a normal distribution with a mean of 54 months and a standard deviation of 8 months.

Also, using the normal model it was determined that 1.22% of graphing calculator manufactured by Texas Instruments malfunctions and needs replacement.

That is,

P (X) = 0.0122

Texas Instruments has sold 75 million graphing calculators world- wide.

Compute the expected number of graphing calculators that malfunctions within 3 months and need to be replaced as follows:

E (X) = n × P (X)

        = 75 × 10⁶ × 0.0122

        = 915000

Thus, the expected number of graphing calculators that malfunctions within 3 months and need to be replaced is 915,000.

in the math equation 8 x 7 = 56, the 8 and the 7 are both factors of 56, since in this lesson we will use square tiles to figure out the factors of a whole find as many different arrays as you can, but follow one important rule: all the rows must have the i can make two rows of nine, so 2 and 9 are both factors of 18.

step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it