Question

Use technology or a z-score table to answer the question.

The expression P(z<1.45) represents the area under the standard normal curve below the given value of z.

What is P(z<1.45)?

Answer 1

Answer with explanation:

We have to find , P (z< 1.45).

Breaking ,z value into two parts, that is , In the column,the value at, 1.40 and in the row ,value at , 0.05,the point where these two value coincide,gives value of Z<1.45.

The value lies in the right of mean.

So, P(z<1.45)=0.9265

In the,Normal curve, at the mid point of the curve

Mean =Median =Mode

Z value at Mean = 0.5000

→So, if you consider , the whole curve,

P(Z<1.45)= 0.9265 × 100=92.65%=92%(approx) because we don't have to consider ,z=1.45.

→But, if you consider, the curve from mean ,that is from mid of the normal curve

P (z<1.45)=92.65% - 50 %

=42.65% =42 %(approx) because we don't have to consider ,z=1.45.

Answer 2

P(z < 1.45) ≈ 0.92647

Explanation:

Several forms of technology are available for finding the area under the standard normal curve. There are probability apps, web sites, spreadsheets, and calculator functions.

Technology requirements

The area under the standard normal curve between two values of z is given on many spreadsheets and by many calculators using the normalcdf(a,b) function. In this form, 'a' is the lower bound, and 'b' is the upper bound of the z-values for which the area is wanted.

For the problem at hand, the value of 'a' is intended to be negative infinity. A calculator allows input of no such value, so some "equivalent" value must be used. (At least one calculator manual suggests -1e99.)

The area of the normal curve below z=-8 is less than 10^-11, so -8 is a suitable stand-in for -∞ on a calculator that displays a 10-decimal-digit result. All the decimal digits shown are accurate, not affected by our choice of lower bound.

Calculator value of P(z < 1.45)

The attachment shows the value of the expression is about ...

P(z < 1.45) ≈ 0.92647