Question

Question 13 4 pts Assume the amount of time statistics students spent studying for the Math 10 final exam is exponentially distributed with a mean of 4.2 hours. The probability that a student studied between 3 and 5 hours is O 0.4762 O 0.3789 O 0.1855 O 0.6211 Question 14 4 pts In October 2003 the mean sale price of a single family home in Santa Clara County was $683,008. We are interested in determining whether the prices in Cupertino were greater than the county average. We randomly survey 10 Cupertino single family home sale prices in the same time period and find a mean of $703,329 and a standard deviation of $21,403. The appropriate hypotheses are: H.:|2 683,008 H,:!<683,008 °H:45 703,329 H,:> 703,329 O H.:| 683,008 H,:| > 683,008 0 H.:| < 683,008 H.: 412 683,008

Answer 1

13) The time spent for studying for the maths (X) is exponentially distributed with

Mean = $\frac{1}{\lambda}$ = 4.2 hours

So, the parameter of the exponential distribution will be -

$\lambda = \frac{1}{4.2} = 0.24$

P(3 < X < 5) = P(X < 5) - P(X < 3) $= \int_{0}^{5}\lambda. e^{-\lambda.x} - \int_{0}^{3}\lambda. e^{-\lambda.x}$   $= \int_{0}^{5}(0.24)* e^{-0.24x} - \int_{0}^{3}(0.24)*.e^{-0.24x}$

= 0.6988- 0.5132

= 0.1856

Hence, the option (c) is the correct option.

14) Appropriate hypothesis are -

Ho : $\mu\leq 683,008$

Ha : $\mu > 683,008$

Hence, option (c) is the correct option.

Usually what we wish to know is kept in alternative hypothesis, here we wishe to test whether prices in Cupertino was greater than country average (683,008)