(a) what is the probability that a bolt selected at random has a diameter

(i) less than 89mm

(ii) between 89mm and 102mm

Constant uses puts the machine out of adjustment. Every week 100 bolts are tested to ensure that the machine is operating to its required level of performance. The results are summarized in the table below.

Frequencies	Observed Frequencies
D < 90	29
90 < D < 100	33
100 < D < 105	18
105 < D < 110	9
Totals	100

(b)Assuming that the machine produces bolts in a normal distribution, determine the expected frequency.

The Chi-Squared test for goodness of fit is used to determine the whether the sample fits the required distribution.

(c) (i) Write the null hypothesis and alternatve Hypothesis for the test.

(ii) Calculate the chi-squared statistic

(iii) Determine, to a 5% significance level, the machine needs to be adjusted. Justify you answer.