Question

the normal distribution with mean and standard deviation is a good description of the iowa test of basic skills (itbs) vocabulary scores of seventh-grade students in gary, indiana. call the score of a random chose student x for short. calculate . round to 4 places after the decimal point.

Answer 1

The event that student has a score of 10 or higher is : P(Z >= 10). The probability that student has a score of 10 pr higher is 0.0228

Using the Zscore relation ;

• Zscore = (x - μ) / σ

Calculating the Zscore for a score of 10 or higher can be written as :

• P(Z >= 10)

Now we have ;

Zscore = (10 - 6.8) / 1.6 = 2

Hence, Using a Standard normal distribution table;

P(Z >= 2) = 0.02275

Therefore, the probability that student has a score of 10 pr higher is 0.0228

Complete Question :

The Normal distribution with mean 6.8 and standard deviation 1.6 is a good description of the Iowa Test vocabulary scores of seventh-grade students in Gary, Indiana.

(a) Write the event "the student chosen has a score of 10 or higher" in terms of X.

(b) Find the probability of this event.